The Welfare E¤ects of Adverse Selection in Privatized Medicare�

Joshua Lustigy

Yale University

Department of Economics

Version: November 20, 2007

Job Market Paper

Abstract

This paper estimates the welfare losses from market failures caused by adverse selection in privatized

Medicare. I model insurers�premium and coverage choices in an environment where consumers have

heterogeneous preferences and may impose di¤erent costs on their insurers. The model generates predic-

tions about insurers�costs and behavior under varying degrees of adverse selection. I use the model and

exogenous variation in market structure to identify a causal link between consumers�types and insurers�

costs. From the estimated parameters, I can infer whether consumers�preferences, which determine how

much insurance they purchase, contain information about their expected health. The empirical results

imply that adverse selection is indeed present in privatized Medicare. It is more costly to insure con-

sumers with strong preferences for health insurance. With the estimated model, I simulate new equilibria

after removing the distortionary e¤ects of adverse selection from insurers�costs and incentives. The new

equilibria exhibit more generous insurance coverage and lower premiums. These e¤ects are particularly

strong in markets with many insurers. The total surplus associated with privatized Medicare increases

by 14.5%, suggesting that the welfare losses from adverse selection are substantial.

�I am indebted to my advisors, Steven Berry and Philip Haile for their continual guidance, support, and encouragement. Ialso bene�ted from constructive conversations with Fiona Scott-Morton, and my colleagues Jacob Gramlich, Katrina Jessoe,Ying Fan, Allesandro Bonatti, and Maher Said. Special thanks also go to Lyle Nelson at the Conressional Budget O¢ ce forgreatly improving my understanding of Medicare.

yDepartment of Economics, Yale University, 28 Hillhouse Ave., New Haven, CT 06511; joshua.lustig@yale.edu;http://pantheon.yale.edu/~jdl57/

1 Introduction

Since Akerlof (1970) and Rothschild and Stiglitz (1976) �rst formalized the theory of adverse selection,

theorists have emphasized the market failures that adverse selection can cause in insurance markets. Sub-

sequent to these theoretical contributions, an empirical literature emerged that tests for adverse selection

using consumers�observed insurance choices and their risk outcomes.1 Recently, methods to detect adverse

selection and distinguish it from other information asymmetries have grown increasingly sophisticated.2 De-

spite these advances, the current literature remains unable to quantify the market failures emphasized in the

theory.3 Market failures from adverse selection arise from distorted insurer behavior, and thus, measuring

them necessitates a model of insurer behavior. This paper makes two contributions to the adverse selection

literature: �rst, I provide evidence of adverse selection in privatized Medicare, and more importantly, I

estimate the welfare losses from the resulting market failures.

I estimate a model in which insurers choose how much coverage to o¤er and what premiums to charge

under varying degrees of adverse selection. Using insurers�optimal premium and coverage choices, I calculate

insurers�costs of providing insurance coverage. To measure adverse selection, I relate these costs to enrollees�

preferences for insurance, which are hidden from insurers but can be inferred using a model of consumer

sorting. The exercise enables me to detect the presence of adverse selection. Speci�cally, do consumers�

preferences for insurance, which determine how much health insurance they purchase, contain information

about their expected health?

Estimates of insurers�costs con�rm that consumers with strong preferences for generous insurance are

more costly to insure. Market failures arise from this adverse selection because insurers are unable to charge

di¤erent premiums to enrollees with di¤erent unobserved health. Ine¢ cient pricing leads some consumers to

purchase suboptimal levels of insurance to avoid subsidizing the unhealthy.4 Insurers have similar incentives

to avoid the unhealthy, and may distort their plans away from generous coverage to deter their enrollment.

To quantify these distortions, I remove the e¤ects of adverse selection from insurers� costs and use the

estimated model to simulate how insurers�plans and consumers�choices (and therefore, welfare) change in

equilibrium. I �nd the e¤ects of adverse selection to be substantial; after its removal total surplus increases

by 14.5%.

I apply my model to an insurance market where policy makers are increasingly introducing competition:

the market for the provision of managed care options to Medicare bene�ciaries. Between 2000 and 2003,

1 Standard models of insurance markets predict a positive correlation between insurance coverage and risk outcomes thatcan be tested with consumer data. See for example, Chiappori and Salanie (2000) and Cutler and Zeckhauser (2000). Thelatter documents a substantial literature con�rming this positive correlation in health insurance markets.

2Finkelstein and Poterba (2006) test for adverse selection using consumer observables that determine insurance coveragebut are not used by insurers when setting prices. Cardon and Hendel (2001) use a structural model of consumer behavior toseparately identify moral hazard and adverse selection.

3One exception to this is Einav, Finkelstein, and Schrimpf (2007). This paper estimates the welfare costs of adverse selectionin a UK annuity market.

4 If adverse selection is severe, insurers may be unable to simultaneously o¤er generous insurance and attract healthy (i.e.pro�table) enrollees. Markets for generous insurance may unravel. Cutler and Reber (1998) provide evidence of such anunravelling in a Boston insurance market.

2

the Medicare + Choice program (M + C) allowed Medicare enrollees to opt out of traditional, fee-for-service

Medicare and enroll in plans o¤ered by private insurers.5 Participating insurers, mostly Health Maintenance

Organizations (HMOs), agreed to provide the same coverage as traditional Medicare in exchange for payments

from the federal government. Insurers could also o¤er coverage not included in traditional Medicare, such as

prescription drug coverage, and charge enrollees a monthly premium. Underlying the M + C program was

the belief that competing HMOs could more e¢ ciently provide insurance coverage to the nation�s elderly.

The M + C market is one with endogenously di¤erentiated products. HMOs choose how many plans

to o¤er, how much insurance coverage to provide, and what premiums to charge. I assume HMOs�deci-

sions to o¤er prescription drug insurance and other forms of coverage are made simultaneously in a static

setting characterized by a Nash equilibrium. I model consumers�enrollment decisions with a discrete choice

framework. Consumer sorting between HMO plans and traditional Medicare depends on a distribution of

preferences for insurance as well as consumers�choice sets. The model�s structure allows me to infer insurers�

costs and to make predictions about consumer sorting across insurance plans. These form the basis for my

measure of adverse selection.

To measure adverse selection, I estimate a causal relationship between consumers�preferences (implied by

their enrollment decisions) and insurers�costs (implied by their coverage and premium choices). If attracting

consumers with strong preferences for insurance coverage causes insurers to have high costs, then consumers

with strong preferences must tend to have poor expected health. If consumers� preferences depend on

characteristics such as risk aversion, in addition to unobserved health, my model could estimate a negative

relationship between insurers�costs and consumers�preferences.6

My estimation strategy is complicated by unobserved factors that also a¤ect insurers�costs, including

moral hazard. Consider the set of HMOs that o¤er generous prescription drug coverage. These insurers

will attract many consumers with strong preferences for insurance, who may or may not have poor expected

health. If moral hazard is present, hidden action will make these consumers appear costly, independent

of adverse selection. Similarly, insurers� implied costs become uninformative about adverse selection if

unobserved costs in�uence insurers�coverage decisions. Insurers o¤ering generous prescription drug coverage,

for example, may have advantageous relationships with drug companies that I am unable to observe.

Thus, my strategy to identify and measure adverse selection exploits a relationship between adverse

selection, insurers�costs, and variation in market structure. If and only if adverse selection exists, insurers

that enroll many consumers with weak preferences for insurance (and therefore, good expected health) will

have lower average costs. Markets with distinct structures provide insurers di¤erent opportunities to attract

these consumers. In markets with few insurers, for example, HMOs o¤ering generous insurance coverage

attract more consumers with weak preferences for generous insurance. In markets with more insurers,

however, the product space becomes saturated and these consumers are lost to plans that are less generous

5Medicare is a federal program that provides health insurance to the elderly and disabled.6Fang, Keane, and Silverman (2004) and Finkelstein and McGarry (2006) �nd evidence of adverse selection in unobserved

health, but advantageous selection in other characteristics, such as risk aversion, income, and cognitive ability. Advantageousselection exists when consumers enrolling in generous insurance have good unobserved health.

3

and less expensive. I use exogenous variation in market structure and insurers�characteristics to generate

observable variation in sorting by consumers with weak and strong preferences for insurance. My measure

of adverse selection is identi�ed using only the portions of insurers�costs that are explained by this variation

in preference-based sorting.7

Estimates of HMOs�cost functions provide evidence of adverse selection. An HMO�s variable costs of

coverage are 7.4% higher for a consumer whose preferences imply a willingness to pay for insurance that is one

standard deviation above the median. Below, I use my model of insurer and consumer behavior to quantify

the distortions that result from this di¤erence in costs. I remove adverse selection from privatized Medicare

by simulating policies that implement perfect risk adjustment. Government payments to each insurer are

adjusted to re�ect the characteristics of enrollees that they attract. Insurers that attract costly enrollees are

compensated with higher payments, and insurers that attract inexpensive enrollees receive lower payments.

This policy removes the distortionary e¤ects of adverse selection on insurers�costs (and therefore, incentives),

and is an extreme version of policies the government has experimented with in privatized Medicare in recent

years.

Removing adverse selection requires government expenditures on privatized Medicare to increase by

1.7%. But I �nd that its removal induces insurers to expand their insurance coverage and reduce the

premiums they charge, particularly for the most generous plans. Consumer surplus and insurer pro�ts both

increase substantially, o¤setting the increase in government expenditures. Consumer surplus increases from

expanded insurance coverage and lower premiums, and insurer pro�ts, from expanded consumer participation

in privatized Medicare and more generous government payment rates. The total surplus associated with

privatized Medicare increases by 14.5% relative to an equilibrium with adverse selection. Equivalently,

surplus increases by an amount equal to 1% of the government�s total payments to insurers in the initial

equilibrium. These surplus gains are concentrated in markets with many HMOs. Where one HMO operates,

total surplus increases by $7.89 per Medicare bene�ciary per year. In markets with six or more HMOs, total

surplus increases by $20.17 per Medicare bene�ciary per year. These results suggest that the government�s

recent attempts to implement risk adjustment in privatized Medicare are welfare enhancing.

The remainder of the paper proceeds as follows. Section 2 describes the M + C program�s relevant

institutional details and Section 3, the data sources that I exploit. Section 4 describes my model of consumer

and insurer behavior in privatized Medicare and Section 5 discusses my estimation strategy. Section 6

provides a series of tables describing privatized Medicare between 2000 and 2003. Sections 7 and 8 present

the parameter results and counterfactual simulations. Section 9 concludes.

7Moral hazard takes place after contracting is completed. Thus, an insurer�s costs that are attributable to moral hazarddo not depend on market structure. They depend only on the insurer�s plans�characteristics. Similar intuition was used byCardon and Hendel (2001) to distinguish between adverse selection and moral hazard.

4

2 Medicare + Choice Program

Introduced in 1965, Medicare is the primary form of health insurance for the elderly and disabled. It is

presently one of the federal government�s largest programs and constitutes a large portion of total health

care spending.8

In 1982, Congress passed the Tax Equity and Fiscal Responsibility Act, mandating the provision of

managed care options to Medicare bene�ciaries.9 Since then, private insurers have played a continuous role

in Medicare. This paper studies the years between 2000 and 2003 when the program governing privatized

Medicare was called Medicare + Choice and HMOs were the dominant �rm type.10 ,11 Under M + C,

Medicare bene�ciaries could opt out of traditional Medicare and receive health insurance from a quali�ed

private insurer. Insurers wishing to enroll Medicare bene�ciaries signed contracts with the Center for

Medicare and Medicaid Services (CMS) describing what coverage they would provide, and at what costs. A

minimum set of bene�ts were required, essentially equal to the coverage included in traditional fee-for-service

Medicare.12 In exchange, the CMS made per-capita payments to each insurer under contract. Insurers had

the option of providing additional bene�ts, such as (but not limited to) prescription drug, dental and vision

coverage, as well as preventative care, in exchange for monthly premiums paid by enrollees.

Under M + C, it was believed that competitive pressures would induce insurers to submit proposed

contracts that would achieve cost savings for the Medicare program. In addition, Medicare bene�ciaries

would bene�t from coverage more generous than traditional Medicare.13 This logic extended even to markets

with few participating insurers, where insurers�plans still faced competition from traditional Medicare. Most

participating insurers did o¤er plans with coverage not provided by traditional Medicare. In markets with

one insurer, for example, 61% of insurers o¤ered some supplemental prescription drug coverage between 2000

and 2003.

Until 2000, government payments to insurers were set equal to 95% of the expected cost of treating a

bene�ciary within traditional Medicare.14 Policy makers were aware of potential selection problems within

privatized Medicare and between traditional and privatized Medicare. Between 2000 and 2003, the CMS

began to experiment with expanded risk adjustment. The Balanced Budget Act of 1997 (BBA) dictated

that payment rates to insurers re�ect enrollees�lagged inpatient hospital experiences. During the sample

8Spending on Medicare in 2003 totaled $315 billion and in 2002, Medicare accounted for 19% of total spending on personalhealth care and 2.6% of GDP (Medpac 2004).

9HMO participation in Medicare began in 1972. Participation, however, was minimal until TEFRA.10Participation by Preferred Provider Organizations (PPOs) was beginning to develop and Private Fee for Service insurers

(PFFS) were still in their infancy.11The 2003 Medicare Modernization Act rede�ned and expanded the role played by private insurers, relabeling the program

"Medicare Advantage" and adding a prescription drug component to the program.12Traditional Medicare is comprised of two parts, A and B. Part A covers hospital services and enrollment is automatic.

Part B covers outpatient services. Enrollment is not automatic and requires a monthly payment by enrollees, but it is heavilysubsidized by general tax revenue. Virtually all Medicare bene�ciaries enroll in Part B.13"Over time, participating plans will be under competitive pressure to improve their bene�ts reduce their premiums and cost

sharing, and improve their networks and services, in order to gain or retain market share" (Medicare Managed Care Manual,CMS)14Adjustments to payments were made according to enrollees�age, gender, and eligibility status. These adjustments accounted

for little of the variation in realized costs. Most studies estimated that this crude system of risk adjustment accounted for only1-2% of the variation in realized costs (Medpac 2000).

5

period, payments were weighted averages of the pre-BBA rate (90%) and the newer model (10%).15

To redistribute HMO participation geographically, the BBA reduced linkages between payment rates

and the costs of care in traditional Medicare. Pre-BBA payments rates varied considerably across di¤erent

portions of the country due to variation in demographics and medical provider characteristics. As a result,

some markets were heavily underserved by Medicare HMOs. The BBA reduced this geographical variation

in payment rates to increase HMO participation in rural areas.16

Contracts between the CMS and insurers were determined on a county and yearly basis after CMS

payments rates were announced in each county. Once contracting between insurers and the CMS was

completed, Medicare bene�ciaries chose to remain in the traditional Medicare program or enroll in a private

plan o¤ered in their county. HMOs were not allowed to discriminate between bene�ciaries within a market.

Rather, insurers had to o¤er the same menu of plans to all individuals residing in the same county. Nor were

they allowed to terminate a plan, increase premiums, or reduce coverage within a calendar year.17 Most

bene�ciaries that remained in traditional Medicare also enrolled in the voluntary part B component, and

many enrolled in a supplementary Medigap plan.

3 Data Sources

This paper combines data from multiple sources. Insurers�plan characteristics (and bene�ciaries�choice

sets) are retrieved from the Medicare Compare databases for the years 2000-2003. Market share data and

individuals�plan choices are taken from the CMS State-County-Plan (SCP) �les and the Medicare Current

Bene�ciary Survey (MCBS). HMO operating and �nancial characteristics are retrieved from the Weiss

Ratings Guide to HMOs and Health Insurers. I extract market characteristics from the US Census and the

American Hospital Association Directory. Variable de�nitions and construction of the �nal data set are

discussed in the appendix.

3.1 Medicare Compare Databases

The Medicare Compare Database is released each year to inform Medicare bene�ciaries which private insurers

are operating in their county, what plans they o¤er, and what bene�ts and costs are associated with each

plan. For each plan, I collect information on dental coverage, vision coverage, brand and generic prescription

drug coverage, and the copayments associated with prescription drugs, primary care doctor and specialist

visits, and inpatient hospital admissions.

15The newer PIP-DCG risk adjustment model, which re�ects inpatient hospital experiences, has been estimated to accountfor only 5-6% of variation in total health care costs (Medpac 2000).16Payment rates were set to the maximum of a national �oor rate, an updated pre-BBA rate, and a third blended rate.

(Medpac, 2001)17They could, however, increase coverage or reduce premiums.

6

3.2 CMS State-County-Plan Files

The SCP �les provide market share data at the insurer-county-year level for all insurers in all counties. In

each county-year, the SCP �les also inform me how many residents are eligible for Medicare and the average

CMS payment rate. Unfortunately, enrollment information is not provided at the plan level. For insurers

o¤ering multiple plans in a county, the market shares sum across the individual plan shares.

The SCP exaggerates entry because Medicare bene�ciaries are not required to change insurers after

moving across counties. In each county, the SCP lists all insurers with at least one enrollee, even those not

under contract with the CMS. To alleviate this problem, I eliminate all insurers with less than a 1% county

market share. In addition, to be included as a participant in a county, an insurer must be listed in the

Medicare Compare Database.

3.3 MCBS Survey

The Medicare Current Bene�ciary Survey tracks the behavior of a representative national sample of the

Medicare population. Using the 2000-2003 versions of the MCBS, I match a sample of Medicare bene�ciaries,

many observed in multiple years, to speci�c insurance plans. The MCBS helps me overcome the lack of

plan market share data in the SCP �les.

MCBS administrative data informs me which M + C insurer each respondent is enrolled in. The Health

Insurance section asks respondents speci�c questions about their Medicare managed care plan: whether

dental, vision, or prescription drug coverage is provided, and what premiums are charged. Using answers

to these questions, I identify which plan each respondent is enrolled in. The data set also informs me which

county each respondent lives in. With the Medicare Compare Database, I construct choice sets for each

MCBS respondent.

3.4 Weiss Ratings�Guides

Many types of insurers participate in M + C. Large, national companies such as Blue Cross and Blue Shield

and Aetna o¤er plans in markets across the country. Smaller, regional HMOs o¤er plans in a few contiguous

counties. To capture this heterogeneity, �rm characteristics are extracted from the Weiss Ratings�Guides.

On a quarterly basis, the Weiss guides accumulate �nancial information from approximately 1500 United

States HMOs and health insurers. This �nancial information includes total assets, capital, net income, etc.

For all rated United States HMOs, Blue Cross and Blue Shield plans, and large health insurers, the Weiss

guide gives information on administrative expenses, enrollment levels, average medical expenses per enrollee,

and physician network sizes.

7

3.5 Additional Data Sources

Counties with distinct characteristics may impose di¤erent costs on insurers, and contain Medicare bene�-

ciaries with distinct preferences. For each county, I retrieve population, income, and educational attainment

data from the US Census. From the American Hospital Association Directory, I determine how many

hospitals operate in each county.

4 Model

Insurers make entry decisions on a county and yearly basis and Medicare bene�ciaries�choice sets include

the plans available in the county they reside. On this basis, a market is de�ned as a county-year. The

model below describes one market. Insurers decide whether to o¤er plans to Medicare bene�ciaries, what

coverage to provide, and what premiums to charge. Medicare bene�ciaries choose between the plans o¤ered

and traditional Medicare.

4.1 Demand

Assume that consumer i, living in market m, obtains indirect utility from plan k o¤ered by insurer j as

follows:

uijk = (1 + �gi) � gjk + (1 + �pDm + �pi) � �pjk + �mj + "mijk (1)

ui0 = "i0

where

gjk = x0jk � �

xjk; pjk = jk0s observable characteristics

Dm = market m0s demographic characteristics

�mj = j0s unobservable characteristics

"ijk = idiosyncratic ijk horizontal preferences

�i ���Normal(0; �2)�� = i0s unobserved vertical preferences

�p, �, �, � and � are the parameters to be estimated.

Each plan has observable characteristics xjk and pjk. p is the monthly premium. x describes jk0s

coverage and cost sharing requirements. It includes doctor and hospital copayments and variables describing

prescription drug, vision and dental coverage. The characteristics of each plan are collapsed into an index

of overall generosity, gjk = x0jk � �.

8

Medicare bene�ciaries have heterogeneous preferences for insurance generosity and premiums, determined

by the absolute values of draws from a normal distribution and the demographic characteristics of market

m.18 Individuals with large draws of �g gain more utility from plans with generous coverage and are more

likely to enroll in a high g plan than individuals with low �g. Draws of � are positive to ensure that the

marginal utility of insurance coverage and disutility of premiums are positive. The amount of heterogeneity

in preferences is determined by the parameters �2g and �2p. Below, I discuss this heterogeneity further.

Consumers�horizontal preferences vary at the individual-insurer-plan and insurer-market levels. For

the outside good and each plan jk, i receives idiosyncratic type-1 extreme value shocks to utility, "ijk:

Each insurer j has a quality level �mj in market m that provides utility to all Medicare bene�ciaries. It

can contain information the econometrician does not observe (for example, physician network quality or

insurers�experiences in particular markets) and information the econometrician does observe (insurer type).

A regression of �mj on the latter class of data can suggest which variables are correlated with high utility

provision.

4.2 Supply

Insurer j expects to incur a cost cjk��g; g;�

supply�from providing coverage with generosity g to a Medicare

bene�ciary with preferences �g. There is a �xed cost per enrollee, FCjk(�g;�Supply), that does not depend

on g. The remaining variable costs of coverage, MCjk(�g;�Supply) � g, are linear in g :

cjk(�g; g;�Supply) = FCjk(�g;�

Supply) +MCjk(�g;�Supply) � g (2)

= (�0 + 0�g + �00Xm + �

00Zj +

0jk) +

(�1 + 1�g + �01Xm + �

01Zj +

1jk) � g

where

g = amount of insurance coverage (generosity)

Xm = market m0s characteristics

Zj = insurer j0s characteristics

0jk; 1jk = cost shocks to plan jk

�g = consumers�preferences for g

�, , �, and � are parameters to be estimated.

This cost function nests adverse and advantageous selection. If consumers with strong preferences for

18Assuming that i0s vertical preferences depend on observable market, rather than individual, characteristics is an obvioussimpli�cation. I make it because it is di¢ cult to collect distributions of Medicare bene�ciaries�observable characteristics at thecounty level. County distributions are necessary because insurers�choices are made at the county level. In principle, however,collecting this data is possible.

9

insurance coverage (i.e., those most likely to enroll in generous plans) are more costly to insure (adverse

selection), 0 and 1 are positive. If there is a negative relationship between preferences and costs (advan-

tageous selection), 0 and 1 are negative. The signs and magnitudes of 0 and 1 play an important role

in determining the e¤ects of selection in equilibrium.

Each insurer realizes two shocks to costs; 0jk and 1jk for each plan they o¤er. The shocks to FC andMC

are perfectly observed by insurers, but not the econometrician, and are drawn from separate distributions

that are iid and mean zero across insurers and markets.19

Finally, FC andMC depend on exogenous market and insurer characteristics, Xm and Zj . Xm controls

for cost di¤erences across markets and includes information such as average income, population, etc. In

wealthier markets, for example, insurers may need to pay higher wages to local employees. Xm also includes

the number of hospitals in m, yearly dummy variables, current CMS payment rates, as well as the pre-BBA

payment rate. Prior to 1997, this rate perfectly re�ected the government�s costs of providing insurance to

bene�ciaries in traditional Medicare.

Zj includes insurers� �nancial and operating characteristics, such as lagged income and asset levels,

administration costs, �rm type, etc. Z controls for the possibility that heterogeneous insurers draw cost

shocks from distributions with di¤erent means. For example, large insurers may be able to more e¤ectively

negotiate with pharmaceutical companies and therefore, have advantages o¤ering generous drug coverage.

Similarly, insurers with large physician networks may charge enrollees lower copayments for doctor o¢ ce

visits.

4.3 The Order of Decisions

I describe the game that insurers and Medicare bene�ciaries play in four stages:

� Stage 1: Insurers decide whether to enter each market m, and if so, how many plans to o¤er: This de-

cision conditions on observable market characteristics and the observable characteristics of all potential

entrants. � is included in this set.

� Stage 2: After each insurer j commits to o¤er nmj plans in market m, cost shocks 0jk and 1jk are

realized for each plan k:

� Stage 3: After observing competitors� entry decisions and 0jk and 1jk for each jk, each insurer

simultaneously chooses gjk and pjk for each plan k. Insurer j chooses plan characteristics and premiums

to maximize pro�ts in market m.

� Stage 4: Consumers observe g and p for all plans. They choose to enroll in a private insurer�s plan or

remain in traditional Medicare.19The mean zero assumption is without loss of generality.

10

Let MSjk(g; p; � j G;P;�Demand) equal the percentage of Medicare bene�ciaries with preferences, �g,

who enroll in plan jk, conditional on the full set of plans o¤ered, (G;P ). Sm is the per-capita payment made

by the government to insurers in market m. After each insurer chooses g and p and enrollment decisions

are made, j earns pro�ts:

Z�

njXk=1

MSjk(g; p; �jG;P;�Demand) � [Sm + pjk � cjk(�; g;�Supply)]dF (�j�)

I only make assumptions about the timing of insurers�decisions in stages one and two. I assume the

following, however, about insurer behavior in stage three:

Assumption: Conditional on the outcomes of stages one and two, all participating insurers simultaneously

choose gjk and pjk for k = 1; :::; nmj . Choices satisfy a Nash equilibrium, which is assumed to exist.

Characterizing plan characteristics and premiums with a Nash equilibrium condition allows me to exploit

insurers��rst order conditions for g and p in the estimation routine.

Similarly, the game�s four stage structure implies a set of moment conditions useful in estimation. In

particular, Stage 2 implies that conditional on X and Z, the cost shocks, 0 and 1, are independent of the

number of plans and insurers in each market. It is important, therefore, that X and Z adequately control

for di¤erences in costs across insurers and markets.

4.4 Discussion

My model allows consumers only one dimension of preferences for insurance coverage. If there are two

consumers, i and i0, with �gi > �gi0 , then i has stronger preferences than i0 for prescription drug and dental

coverage. A more general environment might allow i to have stronger preferences for prescription drugs

and i0 to have stronger preferences for dental. I impose this restriction to simplify my analysis of insurer

behavior. The restriction implies that the elements of x are perfect substitutes in each plan�s market share

function, since all consumers�willingness to trade between the elements of x depends on the same linear

equation in �. In the appendix, I prove it is without additional loss of generality to assume insurers choose

g, rather than x, for each plan.

A recent empirical literature emphasizes multiple dimensions of consumer heterogeneity, with adverse

selection along some dimensions and advantageous selection along others. For example, risk aversion and

cognitive ability, in addition to unobserved health, may determine preferences for insurance.20 If consumers

have T characteristics that determine their preferences (i.e. �g � �g(ti1; ti2; ::; tiT )), the elements of t may

have di¤erent e¤ects on insurers�costs. For example, ti1 might capture i0s unobserved health and ti2, i0s

risk aversion, which might be correlated with good health. In the appendix, I prove that under certain

distributional assumptions on t and �, my model is equivalent to one with costs that depend on t (i.e.

20See Fang, Keane, and Silverman (2006); Finkelstein and McGarry (2006)

11

c(g; t) = ( 00 � t+ 0) + ( 01 � t+ 1) � g). This result also follows from consumers having one dimension of

preferences for insurance coverage.21

5 Estimation

Let �0 denote the true set of parameters. They are estimated using a simulated method of moments

framework. Estimation is done in one step, but below, I discuss supply and demand separately. Details

are left for the appendix.

5.1 Demand

Let m denote the set of private insurers o¤ering plans in market m, and mj the set of plans o¤ered by

insurer j. The probability that an individual enrolls in plan jk in market m is given by:

Prob(jkjm;�) =

Z�

e(1+�g)�gjk�(1+�pDm+�p)��pjk+�mj

1 +P

j02m

Pk02mj0

e(1+�g)�gj0k0�(1+�pDm+�p)��pj0k0+�mj0

dF (�j�) (3)

=

Z�

euijk(�)+�mj

1 +P

j02m

Pk02mj0

euij0k0 (�)+�

mj0dF (�j�)

=

Z�

Prob(jkj�;m;�)dF (�j�)

In many discrete choice models, equation (3) and market share data are used to identify �. Remain-

ing parameters are then identi�ed by assuming observed product characteristics are mean independent of

�.22 This assumption is inappropriate here, because insurers observe � before choosing premiums and plan

characteristics. Instead, my estimation strategy relies on two restrictions:

1. There is no unobserved quality at the plan level, i.e., �mjk = �mj 8 jk and m:

2. Individuals�vertical preferences, �gi and �pi, do not change over time.

The �rst restriction allows me to identify �, �, and �. The second restriction allows me to identify �.

Below I discuss identi�cation of �. Then I describe how these two restrictions are used to identify �, �, �,

and �:21Since insurers can not discriminate against consumers with the same �, but distinct t, insurers� relevant cost functions

reduce to E[cjk(t; g;�Supply)j �g(t)]. This expected cost is equal to cjk(vg(ti1; ti2; ::; tin); g;�Supply) ifdE[tmjv]

dv= 4m for

all v and m.22See Berry, Levinsohn, and Pakes (2003). Other studies of the Medicare HMO market, such as Town & Liu (2003) and

Maruyama (2006) make similar assumptions.

12

5.1.1 Identifying �

The SCP �les provide market share data at the insurer-market level. Let smj equal insurer j0s market share

in m: Following Berry (1994), for any �, �, �, and �, there exists a unique � such that:23

smj =X

k2mj

Prob(jkjm;�) 8 j and m

5.1.2 Identifying �, �, and �

If insurer j o¤ers only one plan, then for any �, �, and �, there is a �j such that j0s predicted market share

equals his observed market share. Thus, to identify �, �, and �, I use the model to predict the choices

made by MCBS respondents enrolled with insurers that o¤er more than one plan. The probability that an

individual enrolls in plan jk; conditional on enrolling with insurer j in market m; is given by:

Prob(kjj;m;�) =Z�

Prob(jkj�;m;�)Pk2mj

Prob(jkj�;m;�)dF (�j�)

Because there is no unobserved quality at the plan level (the �rst restriction), it is easily shown that �

does not enter Prob(kjj;m;�). The model is forced to rely on �, �, and � to predict within-insurer choices.

For an individual i enrolled with insurer j in market m, let dmijk equal one if i enrolled in plan k and zero

otherwise. dmijk is a random variable with expected value Prob(kjj;m;�0). Across jk, the only source of

variation in dmijk are "ijk draws. Since " draws are independent of plan characteristics and premiums, at the

true parameters the residualhdmijk � Prob(kjj;m;�)

ihas expected value zero and is uncorrelated with plan

characteristics and premiums. The three moment conditions below exploit these properties.

E[xjk � (dmijk � Prob(kjj;m;�0))ji; j;m] = 0 (4)

E[xjkx0jk � (dmijk � Prob(kjj;m;�0))ji; j;m] = 0 (5)

E[pjk � (dmijk � Prob(kjj;m;�0))ji; j;m] = 0 (6)

The intuition behind these moments is best understood after distributing the instruments inside of dmijk�

Prob(kjj;m;�). Equation (4) states that at the true parameters, the model accurately predicts the mean

level of x consumed by j0s population of enrollees. If, for example, the model over predicts the share of

consumers with dental coverage, � is adjusted to correct the discrepancy. Combined with (4), (5) states

that at the true parameters, the model accurately predicts the covariance between characteristics in plans

chosen by j0s population of enrollees.24 The intuition behind (6) is similar to (4). The sample moments

23 � is unique up to a normalization. I normalize the mean utility of traditional Medicare to be zero.24For example, do consumers always choose plans that o¤er dental and vision coverage?

13

sum over the set of MCBS respondents enrolled in each insurer, and then over insurers and markets.25

5.1.3 Identifying �

To identify �, I use the model to predict the choices made by MCBS respondents observed in multiple

markets (i.e. years). Suppose an individual is observed enrolling in plan jk in market m and j0k0 in market

m0 (one year later). The probability of this event is given by:

Prob(jk & j0k0jm;m0;�) =

Z�

Prob(jkj�;m;�) � Prob(j0k0j�;m0;�)dF (�j�)

Because individuals�preferences, �g and �p, do not change over time (the second restriction), Prob(jk &

j0k0jm;m0;�) 6= Prob(jkjm;�) � Prob(j0k0jm0;�). Let dm;m0

ijk;j0k0 equal one if i is observed enrolling in plans

jk and j0k0 in markets m and m0, and zero otherwise. As before, [dm;m0

ijk;j0k0 � Prob(jk & j0k0jm;m0;�)] is

a random variable, and at the true parameters, has an expected value equal to zero. For each individual,

the only source of variation in [dm;m0

ijk;j0k0 � Prob(jk & j0k0jm;m0;�)] across jk and j0k0 are draws of ". This

motivates the following moment condition:

E[xjk � x0j0k0 � (dm;m0

ijk;j0k0 � Prob(jk&j0k0jm;m0;�0))ji;m;m0] = 0 (7)

Condition (7) states that at the true parameter values, the model accurately predicts the covariance

between characteristics of distinct plans chosen by the same individual in multiple years. These moment

conditions are particularly useful for identifying heterogeneity in preferences. As �2g increases, the model

predicts more individuals with strong preferences for insurance coverage. These individuals are unlikely

to enroll in a plan with little coverage in one year and a plan with generous coverage in the next. If,

for example, MCBS respondents are rarely observed switching from plans with unlimited prescription drug

coverage to ones with no drug coverage, this behavior can be explained with a large �2g. A sample version

of (7) is constructed by summing over combinations of plans available to each MCBS respondent, and then

over MCBS respondents observed in multiple years.

5.1.4 Additional Moment Conditions

I construct a �nal set of demand-side moment conditions from the observation that at the true parameter

values, functions of j0s competitors� (denoted by �j) plan characteristics and premiums are uncorrelated

with the residualhdmijk � Prob(kjj;m;�)

i. For example,

E[f(x�jkjxjk) � (dmijk � Prob(kjj;m;�0))jj] = 0 (8)

25The integrals used to construct Prob(kjj;�) do not have closed formed solutions and must be simulated using a sampleof draws from F (vj�). The induced simulation error enters these moments linearly, and therefore does not generate any bias.The sample moments�variances are a¤ected, however. Corrections to these variances are discussed in the appendix.

14

with

fx(x�jkjxjk) = % of plans from � j with x�jk < xjk

fp;x(p�jk; x�jkjxjk) = Mean premiums of � jk with x�jk = xjk

At the true parameter values, equation (8) holds for the same reasons discussed above. At an incorrect

set of parameter values, the residualshdmijk � Prob(kjj;m;�)

imay be correlated with �j0s premiums and

plan characteristics. This occurs because insurers condition on their own and competitors�� before designing

their plans. There may be a relationship between x�jk and �j in equilibrium. For example, if �j is large,

j0s competitors might choose low premiums. At an incorrect �, the Berry contraction mapping generates

an incorrect �, and the residualshdmijk � Prob(kjj;m;�)

ibecome functions of the true �j .

5.2 Supply

In each market the collection of premiums and plan characteristics, fgjk; pjkgjk2m are characterized by a

Nash equilibrium. I assume insurers��rst order conditions with respect to premiums and insurance coverage

equal zero:

@Profitj@gjk

=@Profitj@pjk

= 0 8 jk

A �rm o¤ering nj plans has 2 � nj �rst order conditions that reduce to 2 � nj non-redundant linear

equations in 2 �nj cost shocks, . For each choice of parameters, I invert the insurers��rst order conditions

to recover 0jk and 1jk for each jk. I construct moments from these recovered cost shocks to identify the

parameters in costs, (�0; 0; �0;�0; �1; 1; �1; �1).

5.2.1 Identifying

If adverse (or advantageous) selection exists, insurers�marginal costs are directly a¤ected by the preferences

of consumers they enroll. The parameters of interest, 0 and 1, measure this causal e¤ect. I use �rst

order conditions for g and p to recover insurers�marginal costs, which are a¤ected by adverse selection and

insurers�cost shocks, . Since insurers who realize di¤erent may attract di¤erent types of consumers,

I use exogenous variation in market structure to identify 0 and 1. Below, I explain my identi�cation

strategy and the moment conditions it implies. First, consider a one-plan insurer�s �rst order condition for

generosity, gjk:

15

PjkdMSjk(g; p;�)

dgjk= ( 0 + 1gjk)

Z�

�g �dMSjk(�jg; p;�)

dgjkdF (�j�) (9)

+ 1

Z�

�g �MSjk(�jg; p;�)dF (�j�)

+(e 0jk + e 1jk � gjk)dMSjk(g; p;�)

dgjk+ e 1jkMSjk(g; p;�)

The left hand side of equation (9) is the marginal revenue to j from an incremental change in gjk. The

right hand side captures the marginal cost from an incremental change in gjk. This marginal cost is the

sum of three e¤ects.26

First, increasing generosity changes the pool of enrollees that jk attracts. Increasing g attractsdMSjk(�jg;p;�)

dgjkdF (�j�) new enrollees with preferences �. These new enrollees change the insurer�s costs by

( 0 + 1gjk) �gdMSjk(�jg;p;�)

dgjkdF (�j�). Integrating this indirect cost over � yields the �rst term in the right

hand side of (9). It captures the overall e¤ect on the insurer�s costs from changes in his pool of enrollees. If

increasing gjk attracts many new high �g enrollees, and adverse selection is present, then costs will increase.

If there is no advantageous or adverse selection ( 0 = 1 = 0), then changes in jk0s pool of enrollees do not

a¤ect costs.

Next, increasing gjk has a direct e¤ect on costs. It becomes more costly to insure each of jk0s enrollees,

even those enrolled in jk prior to the increase. If adverse selection is present, it is particularly costly to

provide high �g enrollees with additional g. This e¤ect is captured by the second term in (9). If adverse

and advantageous selection do not exist, this direct e¤ect on costs does not depend on jk0s pool of enrollees.

The third e¤ect on marginal costs is determined by Xm, Zj , 0jk and

1jk.

The terms attached to 0 and 1 in (9) (R��g � dMSjk(v)

dgjkand

R��g �MSjk(�)) are functions of pjk and

gjk. Therefore, they are correlated with 0jk and 1jk since j chooses pjk and gjk after observing

0jk and

1jk. To identify 0 and 1, I use the number of insurers and plans in each market (J and JK), �, and

insurers�opponents�characteristics, Z�j as instruments. The four stage game in section (4) implies �, J

and JK are independent of jk. I assume Z�j is uncorrelated with jk.27 . The instruments are correlated

with the endogenous terms because dMSjk(�)dgjk

and MSjk(�) depend on the entire choice set, not just gjk and

pjk. The instruments a¤ect market structure and competitors�choices, and therefore, the choice set.

There is a relationship between the endogenous term,R��g �MSjk(�), and the instrument, JK, because

consumers�sorting depends on how many plans are available.R��g �MSjk(�), the expected strength of

jk0s enrollees�preferences, is increasing in generosity, at a rate that is increasing in JK. In markets with

many plans, sorting is more e¢ cient, and there is less pooling within plans among consumers with di¤erent

26 In (9), e zjk = �z + �0zXm + �0zZj + zjk for z = 0; 1:27 0jk and

1jk are realized conditional on Zj and Xm, and therefore uncorrelated with Zj and Xm. Therefore, it seems

reasonable to assume Z�j is also uncorrelated with 0jk and 1jk.

16

�g. Low �g consumers are likely to have low coverage, inexpensive plans to choose from, and therefore, will

not enroll in a high g plan. Similarly, high �g consumers are unlikely to enroll in low g plans when the

product space is saturated. A similar relationship between JK andR��g � dMSjk(�)

dgjkcan be derived for any

given gjk.

Intuition also relatesR��g � MSjk(�) to j0s opponents� characteristics, Z�j . Z�j a¤ects g�j , and

therefore, the pool of enrollees that j attracts. Suppose j faces one competitor who o¤ers one plan with

gjk > g�jk or gjk < g�jk. If gjk > g�jk, j will attract more high �g consumers than when gjk < g�jk.

If, for example, Total_Assets�j is positively correlated with g�jk, then Total_Assets�j will be negatively

correlated withR��g �MSjk(�).28 An insurer whose competitor has high assets (and therefore, is likely to

o¤er a generous plan), will tend to draw low �g consumers. Similar relationships can be derived between

Z�j andR��g � dMSjk(�)

dgjk.

The moment conditions used to identify 0 and 1 are listed below.

E[f(Z 0�jm) � njk] = 0 8 j; k; n

E[JKm � njk] = 0 8 j; k; n

E[Jm � njk] = 0 8 j; k; n

E[f(Z 0�jm) � JKm � njk] = 0 8 j; k; n

E[f(Z 0�jm) � Jm � njk] = 0 8 j; k; n

E[�j � njk] = 0 8 j; k; n

E[f(��j) � njk] = 0 8 j; k; n

Sample analogues are constructed by summing across plans, insurers, and markets. Any function f can

be used in these moment conditions. I use Mean (Z�j), Min (Z�j), and Max (Z�j):

0 and 1 are identi�ed only if the sample moments are di¤erent from zero at incorrect guesses of 0 and

1. The mechanical relationships between g and p and the cost shocks , provide intuition for this condition.

Consider an increase in 1 away from its true value. Costs increase, particularly for plans that are attractive

to high �g consumers. The implied cost shocks, , of plans attractive to high �g consumers, must go down

so insurers��rst order conditions continue to hold. If gjk is positively correlated with Total_Assetsj , then

fmean(Total_Assets�j)� 1jk will, on average, be a¤ected by the increase in 1. Consumers with high �g

tend not to enroll in plans o¤ered by insurers with low assets (who o¤er low g plans). Rather, they are

likely to choose plans o¤ered by competitors of low asset insurers. Thus, increasing 1 will increase costs

and decrease most for insurers competing against low asset insurers. This causes the correlation between

fmean(Total_Assets�j) and 1jk to increase away from zero. Similar intuition relates the other moment

28Reduced form regressions of Zj on gjk and pjk are provided in section (8).

17

conditions to 0 and 1.

5.2.2 Identifying �, �; and �

�0 and �1 are attached to constant terms that enter FC(�g;�Supply) and MCjk(�g;�Supply). �0 and �1

are attached to the �rm controls, Zj , and �0 and �1 are attached to market controls, Xm. The following

moment conditions are used to identify �, � and � :

E[ njk] = 0 8 jkn

E[Xm � njk] = 0 8 jkn

E[Zj � njk] = 0 8 jkn

For any choice of , a �, �, and � that satisfy the sample versions of these moment conditions can be

retrieved using an ordinary least squares regression. Let e 0jk and e 1jk be de�ned by:

e 0jk = �0 + �00Xm + �

00Zj +

0jke 1jk = �1 + �

01Xm + �

01Zj +

1jk

I invert insurers��rst order conditions to recover e jk. OLS regressions of e jk on a constant, Xm, and

Zj generate estimates of �, �, and �.29

5.3 Summary of Estimation Routine

The estimation routine is simulated method of moments. It searches over (�; �; �; �; ) for the minimum of

a criterion function, (�; �; �; �; ):

(�; �; �; �; ) = 24Demand_Moments(�; �; �; �; )

Supply_Moments(�; �; �; �; )

350 �W�

24Demand_Moments(�; �; �; �; )

Supply_Moments(�; �; �; �; )

35Evaluating can be broken into four steps for each choice of (�; �; �; �; ) :

1. Use the Berry contraction mapping to generate b�(�; �; �; �; )2. Plug b� into the insurers��rst order conditions and back out e :

29This method is not asymptotically e¢ cient. A weighted IV regression using Xm, Zj , and Z�j is implied by the GMMcriterion function. In practice, this regression has little e¤ect on parameter estimates and the standard errors.

18

# Insurers 2000 2001 2002 2003 Total1 607 517 581 722 24272 560 522 333 434 18493 784 405 244 351 17844 373 131 81 127 7125 266 107 27 30 4306 195 43 13 42 293

>6 136 108 83 112 439Total 2921 1833 1362 1818

Table 1: Total Number of Markets

3. Regress e on a constant, Xm and Zjm to �nd (b�0; b�1;b�00;b�01; b�00; b�01) and j4. Evaluate the remaining supply and demand moment conditions and calculate the value of at

(�; �; �; �; ):

The market share probabilities and insurers�cost shocks are continuous in the parameters. In the text

above, intuition for identi�cation was given. Assuming standard regularity conditions yields consistency of

the parameter estimates and their asymptotic distribution (Newey & McFadden 1994).

6 Descriptive Results

The tables in this section describe insurers, the markets insurers participate in, and the plans that insurers

o¤er. Tables 1 displays the distribution of insurers across markets and across time. The majority of markets

have at least two insurers, but the overall trend in insurer participation is negative. HMO participation was

at its strongest in 2000, when payment rate reductions put in place by the BBA began to take e¤ect.30 In

2003, the Medicare Modernization Act was passed, paving the way for expansions in privatized Medicare.

Table 2 displays the characteristics of markets that have di¤erent numbers of insurers. There are strong

correlations between the number of insurers in a market and the government�s payment rate, as well as

between the number of insurers and market size.31

Tables 3 and 4 describe the types of insurers participating in Medicare, and their characteristics. Most

are Health Maintenance Organizations, but Preferred Provider Organizations and Private Fee for Service

insurers are becoming increasingly common.32

Table 5 displays means and standard deviations of plan characteristics included in utility. It is through

dental, vision, and prescription drug coverage that private insurers distinguish themselves from traditional

30The BBA reduced payments on average to insurers by 6% (Congressional Budget O¢ ce 1999).31Maruyama (2006) �nds that CMS subsidy rates are an important determinant of entry by Medicare HMOs.32PPOs share characteristics with traditional Indemnity Plans and HMOs. HMOs tend to be restrictive about where enrollees

can receive medical care and traditional Indemnity plans are not. Within PPOs, medical care can be received from all providers,but small penalties are imposed for out of network care. PFFS insurers provide coverage identical to traditional Medicare.

19

# Insurers Payment Rate Outside Mkt. Sh. # Plans in Mkt Mkt Population1 513.70 92.3% 2.06 121.922 526.78 85.5% 3.79 294.403 545.49 77.2% 6.96 442.004 537.97 73.5% 6.36 567.105 582.84 71.4% 8.95 663.706 603.54 72.8% 11.71 1395.16

>6 628.69 65.4% 12.70 3128.84

Table 2: Market Characteristics

Notes: Payment rate is equal to the base subsidy paid per month/enrollee to HMOs by the CMS. Outside Mkt Share equal to thepercentage of enrollees remaining in traditional Medicare. # Plans is equal to the total number of plans offered by insurers.Population is in 1000s.

# Insurers % White Income % BA Degree # Hospitals1 0.91 19.00 18.7% 2.702 0.88 21.23 21.9% 5.263 0.84 23.04 26.0% 7.524 0.85 22.80 25.2% 8.965 0.78 24.43 27.6% 10.766 0.72 23.60 26.9% 19.26

>6 0.71 20.38 23.0% 35.38

Table 2 Ctd.: Market Characteristics

Note: Per Capita Income in 1000's. % BA Degree is the percentage of a market's population with a college degree.

Year % # % # % #2000 92.85% 2200 0.00% 0 7.15% 1342001 93.62% 1273 1.93% 16 4.45% 632002 87.17% 675 1.83% 11 11.00% 1162003 80.52% 868 0.96% 7 18.52% 259

Notes: Table gives distribution of firm types in those markets used in estimation.

HMO PFFS PPOTable 3: Insurer Types

Mean Std. DevTotal Assets $374.63 791.78Net Income $10.82 42.12

# Physicians / Enrollee 47.97 67.01% Administrative Expenses 9.88% 0.94

Medical Expenditures / Enrollee $140.49 189.25% Business Medicare 22.38% 2.17

Table 4: Mean Insurer Characteristics

Notes: All data reported at the insurer level, not the insurer-market level. Assets and Net Income reportedin $Millions. #Physicians/Enrollee is equal to the total number of member physicians divided by the totalnumber of enrollees. Administrative expenses are given as a percentage of total premium income. MedicalExpenditure/Enrollee the average amount spent on each enrollee per month. %Business Medicare is percentof enrollees who are Medicare beneficiaries. All variables lagged one year.

20

Mean Std. DevPremium $56.72 49.68$ Specialist $13.12 9.44Vision 83.10% 3.70$ Inpatient Hospital Admission $90.55 214.53Dental 19.78% 3.98Generic PD 61.32% 4.87Brand PD 50.05% 5.00Generic PD Unlimited Coverage 34.17% 4.74Brand PD Unlimited Coverage 6.44% 2.45$ Copay Brand PD $10.56 15.01

Table 5: Plan Characteristics

Notes: Premium is paid monthly. $Specialist and $Inpatient Hospital are paid when anenrollee visits a specialist or is admitted to an inpatient hospital. Vision, Dental, andPrescription Drug (PD) are dummy variables, indicating whether any coverage is offered.Unlimited coverage variables indicate if there are limits to prescription drug coverage. $Copay Brand PD is enrollee's cost for a 30 day supply of a brand prescription drug. Paymentsall in 2000 dollars

# Insurers Premium Dental Vision $ Specialist1 $68.64 11.21% 71.98% $12.882 $57.55 20.23% 83.23% $13.623 $62.18 20.96% 88.34% $14.264 $42.91 22.47% 90.73% $12.255 $45.19 24.19% 94.19% $12.306 $32.56 30.03% 91.47% $11.77

>6 $14.03 45.45% 94.17% $10.82

Table 6: Mean Plan Characteristics by # Insurers

Medicare.33 The remaining variables proxy for cost-sharing requirements (i.e. copayments) in each plan.34

In particular, there is extensive variation in premiums and the types of prescription drug coverage that are

o¤ered.

Table 6 displays a clear correlation between the number of insurers in a market and the amount of

coverage that insurers o¤er. This re�ects competition, payment rates, and perhaps costs. In markets with

one insurer, the mean monthly premium is $68.64. In markets with six or more insurers, the mean premium

is $14 per month. Similarly, in markets with more insurers, prescription drug, dental, and vision coverage

become more common.33Town & Liu (2003) �nd that the main source of surplus gains from HMO participation in Medicare are utility gains from

prescription drug insurance which was absent from traditional Medicare until 2006.34Clearly, there are more plan characteristics in a typical insurance plan than listed. Unfortunately, reporting methods make

comparison of many plans�characteristics di¢ cult. These variables should serve as a reasonable proxy for each plan�s amountof coverage.

21

# Insurers $ Inpatient Hospital Generic PD Brand PD1 $100.77 46.48% 36.59%2 $86.91 57.00% 46.02%3 $82.09 67.21% 53.53%4 $104.46 74.86% 62.64%5 $31.04 82.79% 73.26%6 $81.97 83.28% 74.74%

>6 $126.02 80.42% 68.07%

Table 6 ctd.

Notes: Same as Table 5

7 Estimation Results

7.1 Utility

The main speci�cation for utility is given in equation (1). Table 7 displays estimates of the parameters

entering this speci�cation.

The parameter estimates have the expected signs and are very precise. In particular, Medicare bene�cia-

ries receive signi�cant utility from prescription drug coverage. The parameters on Generic PD and Brand

PD Unlimited are signi�cant at the 0.1% level. The parameter attached to Generic PD Unlimited is

signi�cant at the 1% level. Brand prescription drug coverage provides little utility beyond what is provided

by generic coverage. This is probably the result of a strong correlation between Generic PD and Brand

PD.

Dental and vision coverage also provide positive utility. The payment variables are negative, as expected.

The parameter attached to $Specialist is not precisely estimated, but utility decreases by a signi�cant amount

when a plan�s inpatient hospital and prescription drug cost-sharing increase.

Utility is decreasing in premiums, although less so in high income markets. To determine bene�ciaries�

sensitivity to premium increases, I calculate the mean semi-elasticity, @MSjk@Pjk

� 1MSjk

. A $1 increase in a

monthly premium reduces enrollment, on average, by :46%. Town & Liu (2003) estimate that a one dollar

increase in all of an insurer�s plans decrease the insurer�s market share by :9%. This elasticity is comparable

to mine since the average insurer o¤ers 1:64 plans.35 I also calculate mean market share elasticities with

respect to generosity and � (@MSjk@gjk

� gjkMSjk

and 1nj

@MSj@�j

� �jMSj

). A one percentage increase in a plan�s

generosity generates, on average, a :98% increase in market share. Increasing unobserved quality by one

percent generates, on average, a :72% increase in market share for each plan.

35Buchmueller (2000) �nd a premium semi-elasticity of -.7%. Atherly, Dowd, and Feldman (2003) �nd -.7% and -.4%. Bothof these studies also examin Medicare bene�ciaries.

22

(1)Plan Characteristics

0.6386(.1182)***

0.269(.1284)**-0.0924(.1316)-0.3626

(.1202)**1.1796

(.1311)***0.1022(.1878)-0.0636

(.0041)***0.1984

(.118)**1.1578

(.1794)***-3.1885

(.1013)***Vertical Preferences

0.2911(.0348)***

0.0000(4.4312)-0.0094

(.003)***

Table 7: Utility Parameter Estimates

Premium

Generic PD Unlimited

$ Inpatient Hosp Admission

Generic PD

Brand PD

$ Brand PD Copay

Dental

Vision

$ Specialist

Notes: Standard errors in parentheses. Variable definitions given in Table 5 and appendix.* Significant at 5% level, ** at 1% level, *** at 0.1% level

Brand PD Unlimited

Sigma2 Generosity

Sigma2 Premium

Market IncomePremium

23

7.2 Willingness to Pay

The bottom portion of Table 6 describes estimated variation in consumers�preferences for generosity and

premiums. �2g is positive and estimated very precisely, suggesting there is heterogeneity in preferences for

insurance coverage. Conditional on income, however, the model does not �nd any variation in disutility

from premiums. The strong correlation between gjk and pjk may prevent separate identi�cation of both

parameters.36

To interpret the economic importance of this heterogeneity, I calculate the willingness to pay for plan

characteristics by consumers with di¤erent �g. After adjusting for normalizations, a Medicare eligible is

willing to pay �(1+�g)�n(1+�Im+�p)�

for one unit of xn. Table 8 provides estimates of the willingness to pay for each

component of generosity at the 10th, 50th, and 90th percentiles of the distribution of �g.

10th Percentile Median 90th Percentile$10.81 $13.78 $19.05(1.89) (2.41) (3.33)$4.58 $5.85 $8.08(2.12) (2.71) (3.74)$0.07 $0.09 $0.12(.11) (.14) (.19)

$0.01 $0.02 $0.02(.004) (.01) (.01)

$19.57 $24.97 $34.52(2.04) (2.64) (3.78)$1.96 $2.49 $3.45(3.10) (3.96) (5.47)$1.07 $1.36 $1.88(.08) (.01) (.14)

$3.23 $4.11 $5.67(1.00) (2.45) (3.49)

$19.42 $24.78 $34.24(2.86) (3.64) (5.01)

Notes: WTP estimates give monthly value (in 2000 $s) to consumer from $1 reductions in payment variables and fullcoverage of indicator variables. It is assumed for each percentile, consumers have median preferences for premiums.Standard errors in parentheses. They are constructed after taking parameter draws (except for Sigma2 Premium) from theirestimated distributions.

$ Inpatient Hospital Admission

PD Generic

PD Brand

$ Copay Brand

$ Specialist

PD Generic Unlimited

PD Brand Unlimited

Table 8: Willingness to Pay Estimates

Dental

Vision

The median consumer is willing to pay up to $13.78 per month for dental coverage. An individual at

the 90th percentile of the �g distribution is willing to pay $5.27 more per month. Medicare bene�ciaries

are not sensitive to changes in doctor visit and inpatient hospital admission copayments. With respect

to prescription drug insurance, a consumer at the 10th percentile is willing to pay $44.18 per month for

prescription drug coverage that includes unlimited generic and branded drugs. An individual at the 90th

36The residuals in the utility function are equal to �g jvg j � g + �p jvpj � �p where vg and vp are drawn from a jN (0; 1) jdistribution. With perfect correlation (g = �p), the residuals are equal to (�g jvg j+ �p jvpj) � (�+ �)p, in which case �g and�p are not separately identi�ed. The estimation routine chooses a c�g > 0 and c�p � 0, through the supply side. If adverseselection is an important determinant of �rm behavior, c�g = 0, would not allow my model to capture it.

24

# Insurers CS/Medicare Beneficiary CS/M+C Enrollee$19.85 $251.98(1.248) (12.117)$45.29 $265.33(1.908) (12.577)$70.17 $285.89

(3.108) (13.356)$82.12 $290.53(3.636) (13.407)$88.44 $307.96(4.260) (13.981)$90.40 $293.12(3.792) (13.162)$109.40 $293.12(4.824) (13.456)$59.48 $276.45(2.604) (10.659)

Notes: Column 1 gives yearly value in year 2000 dollars to a representative consumer from living in market with N insurers instead of zeroinsurers. Column 2 gives the total surplus per consumer actually enrolling in a private insurer. Values are population weighted means.Standard errors of means, calculated by taking draws from estimated distribution of parameters, are in parentheses.

Table 9: Consumer Surplus Estimates

1

2

3

4

5

6

>6

Overall

percentile is willing to pay $77.88 per month for the most generous prescription drug package.

7.2.1 Consumer Surplus Estimates

Table 6 shows a relationship between the number of insurers in a market, generous coverage, and lower

premiums. Through improved coverage, lower premiums and plan variety, Medicare bene�ciaries will extract

more surplus from the M + C program in markets with more insurers. Table 9 re�ects this. Following

Train (2003), the expected consumer surplus a representative Medicare bene�ciary receives in a market m

from the presence of M + C insurers isR

1(1+�pIm+�p)�� log

�1 +

Pjk2m e

ujk(�)�.37

A representative Medicare bene�ciary residing in a market with one insurer receives $19.85 in surplus

per year from the M + C program. In a market with more than six private insurers, $109.40 in consumer

surplus is generated per Medicare bene�ciary per year. The second column of Table 9 calculates the total

surplus in each market per bene�ciary enrolled in a M + C plan. Across all markets and years, the total

contribution to consumer surplus is estimated to be $5.911 billion.38 A breakdown by year is given in Table

10.37Relative to a market with only the outside good.

38Town & Liu (2003) estimate national consumer surplus from Medicare HMOs to $4.061 billion in 2000. Maruyama obtainssimilar estimates of $3.881 and $3.963 billion in 2003 and 2004.

25

Year Total Consumer Surplus2000 $1.8082001 $1.4822002 $1.2422003 $1.379

Overall $5.911Note: Estimates are in year 2000 billions of dollars. Full set of markets usedin calculations

Table 10: Total Consumer Surplus Estimates

Premium41.55

(8.30)***73.32

(10.19)***-5.71

(1.95)**-3.7

(.466)***0.259

(.043)***N 5622

R-Squared 0.629Notes: Insurer controls, market controls, and year dummies omitted from table.Mean vg and generosity constructed from estimated demand parameters. StandardErrors are in parentheses. *,**,and *** indicate significance at the 5%, 1% and0.1% levels

Table: 11 Descriptive Evidence of Adverse Selection:Premiums and Preferences

Mean vg

Generosity

# Insurers

Unobserved Insurer Quality

Constant

7.3 Descriptive Evidence of Adverse Selection

If adverse selection is present, insurers that attract enrollees with strong preferences for insurance have high

costs, all else equal. These insurers will need to charge high premiums. Descriptive evidence consistent

with adverse selection is given in table 11. It displays regression results that relate each premium pjk, to

the mean �g of jk0s enrollees, gjk, �j , the number of insurers in jk0s market, and the full set of market and

insurer controls. There is a strong, positive relationship between pjk and jk0s mean �g.39 , 40 , 41

These regression results, however, are only suggestive of adverse selection because they do not adequately

control for the nature of competition in privatized Medicare or di¤erences in price sensitivities across con-

sumer types. Estimates of insurers�costs are presented in the next section.

39Mean �g is calculated asR� �g�MSjk(�)dF (vjb�)

MSjk40The standard errors in Table 11 have not yet been corrected for simulation error. However, running the speci�cation

several times using di¤erent draws of preferences from jN(0; b�2)j had only slight e¤ects on the parameter estimates.41 When Mean vg is removed from the speci�cation, the coe¢ cient on Generosity is positive.

26

7.4 Costs

The costs to an insurer from o¤ering plan jk to a consumer with preferences for generosity, �g, is given in

equation (2). Table 12 displays estimates of this speci�cation.42

The second row describes parameter estimates relating to adverse selection (c 0 and c 1). Both parame-ter estimates strongly suggest the presence of adverse selection: bene�ciaries with strong preferences for

insurance are more costly to insure. A one unit increase in an bene�ciary�s type �g causes a $22.29 increase

in insurers��xed costs of providing care and a $5.58 increase in insurers�marginal costs of generosity. Both

parameter estimates are signi�cant at the 0.1% level.

Across plans, the mean expected marginal cost to insurers from providing an additional unit of generosity

to a consumer at the 10th percentile of Fg(�jb�) is $22.60 per month. For a consumer at the 90th percentileof Fg (�jb�), this marginal cost is $27.17 per month, 20.3% higher. Fixed costs per enrollee (i.e. they do not

depend on coverage) also vary by �g. For enrollees at the 10th and 90th percentiles of Fg (�jb�), mean �xedcosts are $5,588 and $5,807 per year. These results suggest that a consumer�s preferences for generosity

have an economically larger impact on the marginal costs of generosity than the �xed costs of enrollment.

This conforms with economic intuition. Unhealthy consumers don�t impose large burdens on insurers who

o¤er little coverage.

Dental coverage is equivalent to .64 units of generosity. This implies that net of cost-sharing, dental

coverage typically costs an insurer $173.15 and $208.81 per year for enrollees at the 10th and 90th percentiles

of Fg (�jb�) : Similarly, providing a prescription drug package with unlimited coverage costs insurers $524.32and $630.49 per year for enrollees at the 10th and 90th percentiles of Fg (�jb�) .7.4.1 Firm and Market Controls

The estimated coe¢ cients attached to insurer and market controls in table 12 vary in statistical signi�cance.

Also, some conform with economic intuition and others do not. HMOs appear to have higher �xed and

marginal costs than non-HMOs, and overall costs are lower for large insurers. Insurers employing more

physicians per enrollee behave as if they pay higher costs per enrollee.

These controls� ability to explain costs, however, is unimportant relative to their ability to explain

observed levels of insurance coverage and premiums. It must be true that the elements of Zj are correlated

with j0s plans�characteristics, conditional on Xm. If so, Z�j can be used to generate exogenous variation

in q�j and p�j that identi�es 0 and 1. Table 13 displays results from a regression of qjk and pjk on Zj

and Xm. Insurer characteristics do explain their premiums and chosen levels of insurance coverage.

42At the estimated parameters, I evaluate insurers�second order conditions for g and p to determine whether insurers are infact behaving optimally. All of insurers�choices maximize pro�ts locally, and in most cases, over a wide range of feasible (g; p)combinations.

27

Fixed Cost Marginal Cost of Generosity13.51 13.34

(6.669)** (.08)***Adverse Selection

22.29 5.58(4.43)*** (.38)***

Market Controls9.16 -0.001

(.15)*** (.002)-0.46 0.004

(.12)*** (.002)**-0.01 -0.002(.02) (.0002)***-6.08 3.84

(1.29)*** (.02)***-0.3 0.008

(.14)** (.002)***21.85 0.015

(1.77)*** (.022)22.47 0.008

(2.16)*** (.027)31.78 0.005

(1.89)*** (.024)Insurer Controls

4.118 -0.001(2.83) (.035)-2.88 -0.042

(1.01)** (.013)***-0.03 0.0009(.02) (.0002)***0.69 0.0014

(.16)*** (.002)-9.3 -0.005

(1.16)*** (.014)0.0025 0(.0061) (.0001)-2.33 0.06

(.40)*** (.005)***

Table 12: Cost Parameter Estimates

2003 Dummy

# Hospitals

AB Rate / 10

AB Rate 1997 / 10

Population / 1000

Per Capita Income / 1000

vg

2002 Dummy

Notes: Insurer controls lagged one year. AB Rate and AB Rate 1997 are current and 1997 government payment rates toinsurers. Other variables defined in tables 2 and 4. Estimates of the parameters attached to market and insurer controlsobtained from an OLS regression using implied costs as dependent variables. *,**,*** indicate significance at 5%,1%, and 0.1%levels. Standard Errors are in parentheses.

Constant

2001 Dummy

HMO Dummy

Total Assets ($million)

Net Income ($million)

Medical Expenditures / Enrollee

# Network Physicians / Enrollee

% Administrative Expenses

% Business Medicare

28

Generosity Premium1.22 90.91

(.13)*** (7.68)***Market Controls

0.009 0.469(.003)*** (.17)**

-0.009 -1.34(.002)*** (.134)***

0.001 0.012(.0003)*** (.021)

0.016 11.38(.025) (1.48)**-0.007 -0.429

(.003)** (.163)**-0.59 2.76

(.034)*** (2.04)-0.71 -1.13

(.041)*** (2.49)-0.62 14.86

(.036)*** (2.18)***Insurer Controls

-0.25 -1.99(.054)*** (3.26)

0.052 -1.5(.019)** (1.16)0.0002 -0.026(.0004) (.023)-0.002 0.788(.003) (.188)***-0.096 -11.86

(.022)*** (1.33)***0.0002 -0.004(.0001) (.007)-0.045 -2.9909

(.008)*** (.4601)***N 5622 5622

R-Squared 0.331 0.292

Constant

Medical Expenditures / Enrollee

# Network Physicians / Enrollee

% Administrative Expenses

2001 Dummy

HMO Dummy

Total Assets ($ million)

Net Income ($ million)

Notes: Firm controls lagged one year. Standard Errors are in parentheses. *,**,and *** indicatesignificance at the 5%, 1% and 0.1% levels

% Business Medicare

Table 13: Reduced Form Supply Side Regressions

2003 Dummy

# Hospitals

AB Rate / 10

AB Rate 1997 / 10

Population / 1000

Per Capita Income / 1000

2002 Dummy

29

# Insurers All Insurers 0-25th % Generosity 75-100th % Generosity$22.24 $22.34 $20.43(.019) (.019) (.018)$22.95 $23.44 $22.12(.018) (.018) (.019)$23.97 $23.56 $23.03(.019) (.019) (.019)$23.27 $23.67 $22.85(.019) (.018) (.019)$23.07 $23.43 $21.70(.018) (.019) (.019)$22.04 $22.09 $20.96(.018) (.018) (.018)$21.50 $20.82 $21.37(.018) (.017) (.018)

Table 14: Profit Margins with Adverse Selection

1

2

Notes: Estimates of profit margins are per enrollee and per month at the plan level. Generosity quartiles are formed usingthe distribution of generosity across all markets. Reported values are market share and population weighted means.Standard deviations of means in parentheses

3

4

5

6

>6

8 Counterfactual Simulations

8.1 Adverse Selection and Expected Pro�t Margins

To investigate the economic importance of adverse selection, I �rst examine implied pro�t margins in the

presence and absence of adverse selection costs. To remove insurers�costs from adverse selection, I adjust

government payments to insurers to re�ect the di¤erences in costs across enrollees. Let �g denote the median

draw of �g. Payments for consumers with �g < �g are reduced and payments for consumers with �g > �g

are increased so that c (�g;g) = c(�g; g) for all �g and g.

There are two reasons why insurers o¤ering di¤erent amounts of coverage are a¤ected by adverse selection

di¤erently. First, the costs of insurers who o¤er generous insurance are more sensitive to adverse selection

than insurers who o¤er little coverage. Second, generous insurance plans attract more enrollees with strong

preferences for insurance.

Table 14 displays mean pro�t margins in markets with di¤erent numbers of insurers before adverse

selection is removed from insurers� costs. Column 1 displays mean pro�t margins across all insurers.

Columns 2 and 3 display pro�t margins for plans that o¤er coverage in the bottom and top quartiles of the

distribution of generosity. Table 15 holds premiums and plan characteristics �xed and duplicates table 14

after adverse selection is removed from insurers�costs. All pro�t margins are monthly and per enrollee.

In markets with di¤erent numbers of insurers, pro�t margins are similar at each level of generosity, with

and without the e¤ects of adverse selection. This is because CMS payment rates are higher in markets with

more insurers. Otherwise (holding premiums �xed), margins would decline in the number of insurers, as

expected. Pro�t margins of insurers o¤ering low levels of generosity increase slightly when adverse selection

30

# Insurers All Insurers 0-25th % Generosity 75-100th % Generosity$26.77 $23.47 $34.61(.018) (.019) (.023)$27.71 $23.90 $33.49(.018) (.019) (.022)$29.45 $23.94 $34.08(.019) (.019) (.021)$28.81 $24.07 $34.56(.019) (.019) (.021)$29.48 $23.59 $34.94(.018) (.021) (.021)$28.02 $22.26 $33.72(.018) (.020) (.021)$28.89 $20.49 $33.34(.017) (.018) (.019)

Table 15: Profit Margins without Adverse Selection

1

2

3

4

Notes: Estimates of profit margins are per enrollee and per month at the plan level. Generosity quartiles are formed usingthe distribution of generosity across all markets. Reported values are market share and population weighted means.Standard deviations of means in parentheses

5

6

>6

costs are removed. Generous plans, however, experience large increases in pro�t margins.

Estimates of insurers�costs and the changes in pro�t margins in tables 14 and 15 suggest that insurers

do have incentives to distort their coverage to deter enrollment by consumers with high �g. Below, I

remove the distortionary e¤ects adverse selection has on insurers�incentives and costs. I then allow insurers

to reoptimize their choices of (g; p). Tables 14 and 15 suggest that initially generous plans will be most

a¤ected in a new equilibrium without adverse selection. This exercise is necessary to quantify distortions

to behavior caused by adverse selection, and to measure welfare losses due to its presence.

8.2 Endogenous Plan Characteristics and Adverse Selection

Below, I rearrange an insurer�s cost function to make the costs from adverse selection explicit. As before,

the median consumer type is denoted by �.

cjk(gjk; �g) = ( o�g + 0jk) + ( 1�g +

1jk) � gjk =

( o� + o(�g � �) + 0jk) + ( 1� + 1(�g � �) + 1jk) � qjk

I assume that in a world without adverse selection, cjk(gjk; �g) = cjk(gjk; �) for all �g. The costs imposed

on jk attributable to adverse selection are given by cjk(�; gjk)� cjk(�; gjk) = o(�g � �) + 1(�g � �) � gjk.

Suppose outside policy makers remove a percentage P of these adverse selection costs. Insurers�expected

costs per enrollee, for a given gjk, are adjusted by P �R�MS(gjk; �) � [ o(�g � �) + 1(�g � �)gjk] dF (�j�):

When P = 1, adverse selection has no e¤ect on insurers�costs.43

43There are other ways to remove adverse selection. I could allow insurers to charge individuals with di¤erent vg di¤erentpremiums or I could remove vg from consumers� preferences. The counterfactual policy I employ seems most appropriate

31

8.2.1 Recalculating Equilibria

Under a policy P , insurers�costs are given by:

cjk(g; �g; P ) =� o� + (1� P ) � o(�g � �) + 0jk

�+� 1� + (1� P ) � 1(�g � �) + 1jk

�� g

Holding the number of insurers and plans �xed, a Nash equilibrium can be characterized as a set

(Premium�; Generosity�jP ) ��h�

g�jkm; p�jkm

�k=1:::nj

ij=1::mj

�m=1:::M

such that for all jkm, @Profitjm(Premium�;Generosity�j P )

@gjkm=

@Profitjm(Premium�;Generosity�j P )

@pjkm= 0:

In the data, I observe an equilibrium at P = 0. To determine how (Premium�,Generosity�) will change

in response to a small change in P , I implicitly di¤erentiate the full set of �rst order conditions with respect

to P :44

24 @Premium�

@P

@Generosity�

@P

35 = �24 @FOCPremium

@Premium@FOCGenerosity@Premium

@FOCGenerosity@Premium

@FOCGenerosity@Generosity

35�1 �24 @FOCPremium

@P

@FOCGenerosity@P

35 (10)

Using (10) and (Premium�; Generosity�jP = 0), I can �nd (Premium�; Generosity�jP = !) for a small

!. I then �nd (Premium�; Generosity�jP = 2!). I slowly continue along this path until P = 1.45 I

interpret (Premium�; Generosity�jP = 1) as the result of a set of policy changes that slowly (but entirely)

eliminate adverse selection.46

8.2.2 Equilibrium changes in g and p47

Table 16 regresses equilibrium changes in generosity and premiums on initial plan and market characteristics.

As expected, the simulated equilibria exhibit expanded insurance coverage, particularly for insurers who o¤er

the most generous plans in their market and for those initially enrolling many high �g enrollees (see column

one).

because the CMS has experimented with risk adjustment and it is feasible. In principle, the CMS could implement perfect riskadjustment by compensating insurers ex-post.44 Implicit di¤erentiation yields the changes in (Premium�; Generosity�jP ) in an open neighborhood surrounding P . Con-

ditions for its use are that each �rst order condition and its derivatives with respect to P and (Premium;Generosity) arecontinuous. These conditions are satis�ed.45This path does not necessarily exist. If it does, it is not necessarily unique. After each small change in P , generosity and

premiums are adjusted if necessary to make each �rst order condition hold within a small tolerance. In practice, this processwas time consuming, but not di¢ cult.46 In this experiment, I do not allow plans to exit the market or new plans to enter. The latter seems more likely to occur.

I only allow existing plans to change their characteristics. In future work, I hope to endogenize entry.47The results below are preliminary and may change. As of this version, I have simulated new equilibrium in a randomly

chosen 550 markets in my data-set. The aggregate calculations below extrapolate from these 550 markets to the full set ofmarkets.

32

Change in Generosity Change in PremiumConstant 0.667 -0.014

(.079)*** (.531)# Insurers -0.0004 0.2675

(.005) (.151)Initial Generosity -0.025 -3.28

(.007)*** (.211)***Initial Mean vg 0.484

(.082)***Max G 0.088 0.483

(.036)** (1.13)Max G * Generosity 0.001 -0.559

(.012) (.371)N 2519 2519R2 0.378 0.153

Table 16: Premium and Generosity Changes

Note: Results from an OLS regression. Dependent variables are changes in coverage and premiums after allcosts of adverse selection are removed. Initial Generosity and Mean vg are levels of coverage and enrollees'preferences in original equilibrium. Max G is equal to one if plan was the most generous in its market inoriginal equilibrium. Standard errors in parentheses. *, **, and *** indicate significance at the 5%, 1%, and0.1% levels

When �fty percent of adverse selection costs are removed (P=.50 ), the mean level of o¤ered generosity

increases by .08 units. After all adverse selection costs are removed (P=1), the mean level of o¤ered

generosity increases by .22 units. In almost all markets (87%), the maximum amount of o¤ered coverage

increases; on average, by .33 units. To provide meaning to these unit changes, recall that dental coverage is

equivalent to .64 units of generosity and is worth $13.78 per month to the median consumer.

In the simulated equilibria, I also observe reduced premiums. Mean premiums fall by $.66 and $1.51 per

month after 50% and all of adverse selection costs are removed. These e¤ects are particularly strong for

generous plans (see column two of table 16). When adverse selection is present, generous insurers charge

premiums that re�ect the direct costs of providing generous coverage and the indirect costs of attracting an

unhealthy pool of enrollees. After adverse selection is removed, the latter costs no longer impact insurers�

incentives. The correlation between generosity and premiums is equal to .26 in the original equilibrium.

After adverse selection is removed, the correlation between generosity and premiums falls to .15.48

When the premium schedule �attens, Medicare bene�ciaries consume more generous insurance. The

expected amount of generosity consumed increases by .27 units after 50% of adverse selection is removed,

and by .39 units when it is fully removed.

48 I can not attribute the mean reductions in premiums to adverse selection, because total government payments to insurersincrease. In the future, I plan to implement revenue neutral policies. Adverse selection does explain why generous plans�premiums fall the most in the new equilibrium.

33

8.2.3 Equilibrium Changes in Welfare

The changes in generosity and premiums will bene�t consumers. Medicare bene�ciaries initially enrolled in

M + C plans receive increased utility from expanded coverage and lower premiums. Bene�ciaries originally

in traditional Medicare also bene�t, since the improved menu of plans makes opting out of traditional

Medicare more attractive. Many exercise this option. After adverse selection is eliminated, the percentage

of Medicare bene�ciaries enrolled in a M + C plan increases from 23.9% to 35.2%.49

Insurers�pro�ts also increase. The risk adjustment policy increases payments to all insurers except those

that only attract consumers with weak preferences for insurance. The payment increases o¤set changes in

generosity and premiums that increase costs and decrease revenues. Let (Generosity�,Premium�) and

(Generosity�No Adv Sel ,Premium�No Adv Sel ) denote the equilibrium distributions of generosity and premiums

before and after adverse selection is removed. The change in total welfare per bene�ciary is calculated as

follows:50 ,51

4TW = 4CS +4Profits+4GovtPayments

where

4CS = CS(Generosity�No Adv Sel ;Premium�No Adv Sel )�

CS(Generosity�;Premium�)

4Profits = �(Generosity�No Adv Sel ;Premium�No Adv Sel ; P = 1)�

�(Generosity�;Premium�; P = 0)

4GovtPayments = �(Generosity�No Adv Sel ;Premium�No Adv Sel ; P = 1)�

�(Generosity�No Adv Sel ;Premium�No Adv Sel ; P = 0)

Tables 17 displays yearly changes in total surplus after adverse selection is eliminated from insurers�costs

by perfect risk adjustment. Total surplus increases most in markets with many insurers. This suggests that

welfare losses from adverse selection are larger in markets with more insurers. The mean change in surplus

in markets with one insurer is $7.89 per bene�ciary. In markets with six or more insurers, surplus increases

by $20.17 per bene�ciary. All surplus changes are per year and per bene�ciary.

49The federal government could potentially save money from these enrollment changes if the cost of enrolling bene�ciariesin traditional Medicare is greater than the payment rates made to insurers, even after accounting for risk adjustment. Thewelfare calculations below assume the cost of treating a bene�ciary in traditional Medicare is equal to the payment rate madeto insurers. Thus, these calculations may understate welfare changes. On the other hand, some studies have shown thatthe least costly Medicare bene�ciaries are most likely to enroll in a M + C plan (Hellinger & Wong 2000). In this case, mycalculations may understate increases in government expenditures, and therefore, overstate welfare changes.50 In the simulated equilibria, government expenditures increase. In my welfare calculations, I assume there are no welfare

losses from increases in taxation. This assumption suggests another reason for me to consider revenue neutral risk adjustmentpolicies.51CS(Generosity; Premium) is equal to consumer surplus per bene�ciary given (Generosity; Premium).

�(Generosity; Premium;P ) is equal to the sum of insurer pro�ts per bene�ciary given (Generosity; Premium) and arisk adjustment policy P:

34

# Insurers Original Equilibrium No Adv. Sel. Equilibrium Change$49.64 $57.53 $7.89(6.16) (6.60) (.754)$73.47 $84.43 $10.96(3.19) (3.44) (.528)$99.07 $113.56 $14.49(4.34) (4.81) (.879)

$117.58 $134.64 $17.06(7.63) (8.15) (1.44)

$119.19 $140.64 $21.45(6.22) (7.54) (1.98)

$136.55 $154.35 $17.80(14.13) (14.44) (2.00)$158.76 $178.93 $20.17(18.98) (21.77) (3.86)

Table 17: Changes in Yearly Total Surplus / Medicare Beneficiary

1

2

3

4

5

6

>6

Note: Calculations are per Medicare beneficiary and per year. Means are weighted by number of beneficiaries in each market. Values are in 2000 dollars.Standard deviations of means are in parentheses.

Table 18 decomposes the surplus changes from table 17 into changes in consumer surplus, total insurer

pro�ts, and government expenditures. In each market, government expenditures increase to fund the risk

adjustment policy. To remove adverse selection, government expenditures on privatized Medicare increase

by 1.69%.52 Consumer surplus and total insurer pro�ts, however, increase by amounts that o¤set this

increase in expenditures, and total surplus increases.

Most of the realized surplus gains are enjoyed by Medicare bene�ciaries. In markets with one insurer,

the average bene�ciary realizes an $11.97 increase in consumer surplus, whereas total insurer pro�ts increase

by $7.25 per bene�ciary. In markets with more than one insurer, the relative surplus gains are qualitatively

similar. Consumers consistently realize more gains in surplus than insurers after adverse selection is removed.

Summing across months, markets and the number of Medicare bene�ciaries in each market, aggregate

changes in total surplus are given in table 19. Eliminating the costs of adverse selection increases the total

surplus associated with the M + C between 2000 and 2003 by $1.34 billion. This corresponds to a 14.5%

increase. Equivalently, total surplus increases by an amount equal to 1.0% of total payments made by the

government to M + C insurers before adverse selection was eliminated.

52 Initial government expenditures on M + C are equal to the number of M+C enrollees multiplied by the payment rate.After eliminating adverse selection, expenditures increase by the per bene�ciary change in pro�ts (from Table 18) multipliedby the number of bene�ciaries enrolled in M + C in the new equilibrium. This calculation assumes that the cost of treatinga bene�ciary in traditional Medicare is equal to the payment rate made to M + C insurers. Thus, when bene�ciaries switchbetween M + C and traditional Medicare, the government�s costs do not change.

35

# Insurers Change in CS Change in Profits Change in Govt Exp$11.97 $7.25 $11.32(1.66) (1.22) (2.04)$16.88 $8.98 $14.89(.81) (.56) (.77)

$25.14 $11.14 $21.80(1.38) (.76) (1.09)$29.47 $12.59 $25.00(2.59) (1.57) (1.60)$36.16 $13.74 $28.45(3.58) (1.82) (2.37)$30.76 $14.46 $27.42(3.42) (2.24) (2.60)$36.22 $19.78 $35.84(4.77) (6.03) (5.76)

4

5

6

Table 18: Decomposing Changes in Total Surplus / Medicare Benefciary

1

2

>6Note: Calculations are per Medicare beneficiary and per year. Values for profits sum across all participatinginsurers. All means weighted by number of beneficiaries in each market. Values are in 2000 dollars. StandardDeviations of means are in parentheses.

3

# Insurers Original Equilibrium No Adv. Sel. Equilibrium Change$1,358.887 $1,574.875 $215.988

(168.63) (180.67) (20.64)$1,717.263 $1,973.438 $256.175

(74.56) (80.41) (12.34)$2,051.747 $2,351.836 $300.089

(89.88) (99.62) (18.20)$1,095.625 $1,254.592 $158.967

(71.10) (75.94) 13.42$485.323 $572.665 $87.341(25.33) (30.70) (8.06)

$684.448 $773.670 $89.221(70.83) (72.38) (10.02)

$1,852.798 $2,088.191 $235.393(221.50) (254.07) (45.05)

$9,246.092 $10,589.266 $1,343.174(319.14) (354.30) (57.31)

Table 19: Aggregate Changes in Total Surplus

1

2

3

Note: Changes in TS take changes in TS per beneficiary and multiply by the number of Medicare Beneficiaries in each market. Values in table areconstructed by summing over markets and years. Results are in year 2000 millions of $. Standard deviations of means are in parentheses.

>6

4

5

6

Total

36

9 Conclusion

In this paper, I use observed insurer behavior to investigate welfare losses caused by adverse selection

in privatized Medicare. I estimate a model of privatized Medicare in which insurers choose how much

coverage to o¤er and what premiums to charge, and consumers vary in their preferences for insurance. The

model allows consumers with di¤erent preferences to impose di¤erent costs on their insurers. To measure

adverse selection, I use exogenous variation in market structure to identify a causal relationship between

consumers�preferences and insurers�costs. This strategy allows me to infer whether consumers�preferences

for insurance, which determine how much insurance they consume, contain information about their expected

health. My measure is analogous to previous tests of adverse selection in the sense that I relate consumers�

choices to insurers� costs. But unlike tests that rely only on consumer behavior, my model of insurer

behavior allows me to quantify the welfare losses caused by adverse selection. Market failures caused by

adverse selection begin with distortions in insurer behavior. Measurement of the resulting welfare losses,

therefore, requires a model of insurer behavior.

My empirical results con�rm that consumers with strong preferences for generous insurance are more

costly to insure. Using counterfactual simulations, I �nd that this adverse selection has substantial e¤ects on

welfare. I implement policies of perfect risk adjustment that are extreme versions of policies the government

has experimented with in privatized Medicare in recent years. These policies adjust government payments to

insurers according to the types of consumers they enroll, thereby eliminating the e¤ects of adverse selection

on insurers�costs and incentives. The simulated equilibria exhibit expanded insurance coverage and lower

premiums. Between 2000 and 2003, total surplus associated with privatized Medicare increases by $1.34

billion (14.5%), or equivalently, by an amount equal to 1.0% of the total payments made to insurers by the

government. These results suggest that expanded e¤orts by the government to implement risk adjustment

in privatized Medicare would increase welfare.

Welfare losses from adverse selection are larger in markets with more insurers. In markets with one

insurer, total surplus increases by $7.89 per Medicare bene�ciary in each year. In markets with six or more

insurers, surplus increases by $20.17 per Medicare bene�ciary. These results suggest a tradeo¤ between

the welfare losses from adverse selection and the bene�ts of competition. Welfare in privatized Medicare

could potentially be enhanced if the government limits the number of insurers allowed to enter each market,

but requires each insurer to o¤er more plans. In this paper, I was limited in my ability to consider this

possibility because I took market structure as exogenous. In future research, I plan to generalize my model

so I can further investigate the tradeo¤ between welfare losses from adverse selection and the bene�ts of

competition.

It should also be pointed out that this analysis assumes away consequences from consumers having

multiple dimensions of private information. This omission may be particularly important in scenarios where

consumers with the same preferences, but di¤erent characteristics, impose di¤erent costs on insurers. If

insurers are able to screen along these separate dimensions, the welfare implications may di¤er from those

37

predicted above. In principle, my approach can be used to study the consequences of such heterogeneity.

Thus, this is also a likely avenue for future research.

38

References

[1] Achman, L. and Gold, M. "Trends in Medicare + Choice Bene�ts and Premiums, 1999-2002." Mathe-

matica Policy Research, Inc. November 2002.

[2] Akerlof, G. "The Market for �Lemons�: Quality Uncertainty and the Market Mechanism." Quarterly

Journal of Economics 84(3), pp. 488-500

[3] Atherly, A., Dowd, B., Feldman, R. "The E¤ects of Bene�ts, Premiums, and Health Risk on Health Plan

Choice in the Medicare Program." Mimeo, Division of Health Services Research and Policy, University

of Minnesota, 2003.

[4] Berry, S., "Estimating Discrete-Choice Models of Product Di¤erentiation." RAND Journal of Eco-

nomics, Vol. 25 (1994), pp. 242-262.

[5] Berry, S., Levinsohn, J., and Pakes, A. "Di¤erentiated Products Demand Systems from a Combination

of Micro and Macro Data: The New Vehicle Market," Journal of Political Economy, 112(1), 68-104.

[6] Buchmueller, T.C. (2000) "The Health Plan Choices of Retirees Under Managed Competition." Health

Services Research, Vol. 35, pp. 949-976.

[7] Cardon, J. and Hendel, I. (2001) "Asymmetric Information in Health Care and Health insurance Mar-

kets: Evidence from the National Medical Expenditure Survey." Rand Journal of Economics, 32(3),

408-427.

[8] Chiappori, P., and Salanie, B. (2000), "Testing for asymmetric information in Insurance Markets,�

Journal of Political Economy 108(1), 56-78.

[9] Chiappori, P., Jullien, B., Salanie, B., and Salanie, F. (2006), "Asymmetric information in insurance:

General Testable implications," Rand journal of Economics 37(4).

[10] Cutler, D.M. and Reber, S.J. 1998 "Paying for Health Insurance: The Trade-O¤ between Competition

and Adverse Selection." Quarterly Journal of Economics, Vol. 113 (1998), pp. 433-466.

[11] Cutler, D.M. and Zeckhauser, R.J. "The Anatomy of Health Insurance.", Handbook of Health Eco-

nomics, Vol. 1 (2000), pp. 564-643.

[12] Cutler, D.M. and Zeckhauser, R.J. 1997 "Adverse Selection in Health Insurance." NBERWorking Paper

6107.

[13] Fang, H., Keane, M., and Silverman, D. (2006), "Sources of advantageous Selection: Evidence from the

Medigap insurance market," mimeo, Yale University.

[14] Finkelstein, A., and McGarry, K. (2006) "Multiple dimensions of private information: Evidence from

the long-term Care Insurance Market," American Economic Review 96(4), 938-958.

39

[15] Finkelstein, A., and Poterba, J. (2004), "Adverse Selection in insurance Markets; Policyholder evidence

from the U.K. Annuity Market," Journal of Political Economy, 112(1), 193-208.

[16] Finkelstein, A. and Poterba, J. (2006), "Testing for Adverse Selection with �Unused Observables�."

NBER Working Paper No. 12112

[17] Hellinger, F. and Wong, H. (2000) "�Selection Bias in HMOs: A Review of the Evidence." Medical Care

Research and Review 57(4) 405-438.

[18] Maruyama, S., (2006) "Welfare analysis incorporating a Structural Entry-Exit model: A Case Study of

Medicare HMOs", Working Paper, Northwestern University.

[19] McFadden, D., and Newey, W. (1994) "Large Sample Estimation and Hypothesis Testing", Handbook

of Econometrics. Volume 4, Ch. 36.

[20] Medicare Payment Advisory Commission, (2000). "Report to the Congress: Improving Risk Adjust-

ment in Medicare." Washington, DC: MedPac.

[21] Medicare Payment Advisory Commission, (2001). "Report to the Congress: Medicare Payment Policy."

Washington, DC: MedPac.

[22] Medicare Payment Advisory Commission, (2004). "Report to the Congress: Medicare Payment Policy."

Washington, DC: Medpac.

[23] Moon, M., (2006) "Medicare: A Policy Primer". Urban Institute Press.

[24] Rothschild, M., and J.E. Stiglitz. (1976) "Equilibrium in Competitive Insurance Markets: An Essay on

the Economics of Imperfect information.", Quarterly Journal of Economics, 90(1), 630-649.

[25] Town, R. and Liu, S., (2000) "The welfare impact of Medicare HMOs," Rand journal of Economics,

34(4), 719-736.

[26] Wooldridge, J. "Econometric Analysis of Cross Section and Panel Data." MIT Press: 2001.

40

10 Appendix

10.1 Data

The main sources of data are acquired from the Center for Medicare and Medicaid Services. The data

primarily comes from three sources: the yearly Medicare Compare database, the December version of the

CMS�s State-County-Plan �les, and the MCBS survey. In the CMS data �les, there is a clear distinction

between organizations, contracts, and products. The organization is the broadest of the three and is the

company responsible for overseeing each contract. For example, Paci�care, Aetna, and Humana are all

organizations often observed within the data. In the Medicare program, each organization enters into one

or more contracts with the CMS for the purpose of providing health care to Medicare bene�ciaries. Each

contract is assigned a unique contract number by the government. Often times, organizations enter into

multiple contracts with the government, with di¤erent contracts serving di¤erent markets. Other times, the

same contract extends across markets. Within each contract, organizations o¤er, and Medicare bene�ciaries

can enroll in, multiple products. Products within a given contract can vary along multiple dimensions,

including premiums, copayments, coverage types, etc. In the main text, I assume organizations�behavior is

independent across markets. I refer to a contract as a �rm or insurer and a product as a plan.

10.1.1 Identifying Market Entrants

To identify insurers, I focus on the contract level. The State-County-Plan �les disaggregate enrollment data

at the contract level into enrollment data at the county level. For each Medicare HMO contract, I observe

which counties have a positive number of contract enrollees. If this positive number is greater than ten,

I observe actual enrollment information. Using the SCP data alone, however, greatly overstates entry by

Medicare HMOs. When initially enrolling in a Medicare HMO, bene�ciaries are only able to choose among

those plans o¤ered within their county. But once enrolled, bene�ciaries can remain in a particular plan even

after changing residences. Thus, within the SCP �les, there are many counties that contain information on

the enrollment by Medicare bene�ciaries in a particular contract, despite that contract not being available

within the county. To enter the �nal sample, a contract must be listed as being available in the Medicare

Compare database, and have a market share of at least one percent.

10.1.2 Omitted Plan Types

Under the Medicare + Choice program, several types of private health insurance plans other than Medicare

HMOs are eligible to contract with the CMS to provide coverage to Medicare bene�ciaries. Other types of

organizations include Preferred Provider Organizations (PPO), Provider Sponsored Organizations (PSO),

Private Fee For Service Plans (PFFS), and cost contract HMOs. From a bene�ciary�s point of view, these

plans are full-�edged alternatives to Medicare HMOs as long as they are available in the bene�ciary�s market.

41

They are included in the model.

Other types of plans, however, are excluded from supply and demand. These types include Health Care

Prepayment Plans (HCPP), which cover only outpatient services, Programs of All-Inclusive Care for the

Elderly (PACE), which are combination programs with Medicaid that provide comprehensive community

and medical services (to be enrolled in a PACE plan a Medicare bene�ciary needs to be certi�ed as eligible for

nursing home care by the appropriate state agency), and demonstration plans (DEMO) which are designed

to evaluate the e¤ects and impacts of various health care initiatives.

10.1.3 Plan Characteristics

De�nitions of variables entering Medicare bene�ciaries utility are provided below. All product characteristics

are extracted from the Medicare Compare database.

Premium: Premium information is provided at the monthly level. They do not include the required

payment for Medicare Part B, which is charged to all Medicare HMO enrollees. For a few plans, premium

information was unavailable. These plans were dropped from the �nal sample.

$InpatientHospital: Required payments for inpatient hospital stays varied across plans in structure.

Some described required copayments for days 0�20 and 20�100, others had additional tiers. This variable

is equal to the charged copayment upon admission to an inpatient hospital. For some plans, this information

is explicitly provided in the Medicare Compare Database. For others, the day 1 copayment is used.

$Specialist: Required copayment for each visit to a specialist. Across plans, the format of this data is

constant.

Dental: This is a dummy variable indicating whether any supplementary dental coverage is described in

the Medicare compare database. Traditional Medicare o¤ers no dental coverage. For some plans, additional

information on dental coverage was provided, such as annual deductibles, dentist copayments, etc. But much

of this information was incomplete and its structure varied extensively across plans. If no mention of Dental

coverage was made, I assumed there was none.

V ision: This is a dummy variable indicating whether any supplementary vision coverage is described

in the Medicare compare database. Traditional Medicare o¤ers very little coverage of vision services. The

formats of the data provided was very similar in nature to Dental.

PrescriptionDrugs: Five prescription drug variables were used in demand. First, PDBrand and

PDGeneric are dummy variables indicating whether each plan o¤ered any form of generic and branded pre-

scription drug coverage. Between 2000 and 2003, traditional Medicare o¤ered no such coverage. $BrandPD

is equal to the copayment for a 31 day supply of a brand prescription drug. Some plans described this copay-

ment using di¤erent lengths of time. For these, all copayments were prorated to 31 days. The generosity of

provided prescription drug coverage is captured by UL_BrandPD and UL_GenericPD. Both are dummy

variables indicating whether generic and brand coverage are unlimited. Most plans o¤ered only limited drug

42

coverage, for example $1000 annually. Because of variation in the format of coverage data across plans, it

was di¢ cult to construct additional variables detailing the generosity of any provided drug coverage. If for

each plan, any mention is made of unlimited generic or brand drug coverage these indicator variables are set

to one.

10.2 Firms�Choice Variables

The model assumes insurers choose generosity levels, g, and not the determinants of generosity x. Note

that in insurers�costs and in utility the individual elements of xjk are perfect substitutes. This restriction

implies that it is without loss of generality to assume that insurers choose g. Suppose that insurers did

choose x to maximize:

Z�

MS(g(x); p; �) � [p� c(�; x)]dF (�)

where:

g(x) = �0x

c(�; x) = ( 0� + 0) � [�0x]

Claim 1 If insurers are behaving optimally and for all m and n there exists plans k and k0 such thatxknxkm6= xk0n

xk0mthen �n

�m= �n

�mfor all n and m:

Proof. Assume not. Then for some n and m, �n�m > �n�m: By assumption, there exist plans k and k0 such

that xknxkm

< xk0nxk0m

(i.e. plans k and k0 over xm and xn in di¤erent ratios). If the characteristics in k0 are

optimally chosen, then the characteristics in k are not. Plan k can earn higher pro�ts by increasing xkn and

decreasing xkm. Consider a one unit increase in xkn and a�n�m

decrease in xkm. This shift in characteristics

leaves gk unchanged. Therefore MS(g(xk); pk; �) is unchanged for all �. But pro�t margins will increase.

The e¤ect on costs is negative since:

�n4xkn + �m4xkm =

�n � �m�n�m

< 0 !

�n�m

>�n�m

The last line holds by assumption.

43

Thus, after normalization, insurers� cost functions are equivalent to c(�; g) = ( 0� + 0) � g. Firms

di¤erentiate themselves via choices of overall insurance coverage, not the individual elements of x: It can be

veri�ed that su¢ cient variation in product characteristics exists in the data so that the claim�s assumption

can be veri�ed for each n and m:

10.3 Robustness to Multi-dimensional Types

Suppose that consumers�preferences for generosity are determined by their type ti � (ti1; ti2; :::; tin) so that

(after omitting irrelevant terms) utility is:

uijk = �gi(ti1; ti2; :::tin) � gjk + �pjk + �mj + "mijk

Consumers�preferences for insurance now explicitly depend on their characteristics such as risk type,

risk aversion, cognitive ability, etc. The strong restriction implicit in this speci�cation is that insurers are

unable to screen between consumers with the same � but di¤erent t. This assumption is admittedly strong.

Once it is made, however, it is without loss of generality under certain assumptions to consider the more

general, and realistic, cost function below:

cjk(t1; t2; ::tn; g;�Supply) = (�01t1 + :::+ �0ntn +

0jk) +

(�11t1 + :::+ �1ntn + 1jk) � g

This allows individuals with the same preferences, but di¤erent characteristics, to impose di¤erent costs

on insurers. Because insurers can not discriminate between t conditional on �, their cost function reduces

to a function of E[cjk(t1; t2; ::tn; g;�Supply)j�]. This can be seen by simply rearranging the insurer�s pro�t

function:

Zt1

:::

Ztn

njXk=1

MSjk(g; p; �(t1;:::;tn)jG;P;�Demand) � [Sm + pjk � cjk(t; g;�Supply)]dH(t1; ::tn) =

Ze�

Zt:�(t)=e�

njXk=1

MSjk(g; p; e�jG;P;�Demand) � [Sm + pjk � cjk(t; g;�Supply)]dH(t1; ::tnj�(t) = e�)dF (e�) =Ze�

njXk=1

MSjk(g; p; e�jG;P;�Demand) � [Sm + pjk � E[cjk(t; g;�Supply)j�(t) = e�]]dF (e�)Thus, ignoring the determinants of preferences for insurance can be made without loss of generality if:

44

E[cjk(t; g;�Supply)j�(t) = e�] = cjk(�:g;�

Supply) =

( 0� + 0jk) + ( 1� +

1jk) � g

where

E[cjk(t1; t2; ::tn; g;�Supply)j�] = (�01E[t1j�] + :::+ �0nE[tnj�] + 0jk) +

(�11E[t1j�] + :::+ �1nE[tnj�] + 1jk) � g

Under speci�c conditions on the CDF of t, H(t1; ::tn); this statement is true. Note that cjk(�:g;�Supply)

is linear in � and has an intercept 0jk + 1jk � g when � = 0: Assume that �(t) = 0 if and only if

tm = 0 for each m. Thus, E[cjk(t1; t2; ::tn; g;�Supply)j�] also has an intercept 0jk + 1jk � g when � = 0:

Now, note that cjk(�:g;�Supply) is linear in � with slope 0 + 1 � g. E[cjk(t1; t2; ::tn; g;�Supply)j�] is

also linear in � if dE[tmj�]dv = 4m for all � and each m. For example, if �g(t1; ::; tn) = t1 + :: + tn and

tn~��N(0; �2tn)�� for each n and tn0 is uncorrelated with each tn, this linearity condition holds. The slope of

E[cjk(t1; t2; ::tn; g;�Supply)j�] in � is now equal to (�0141+ :::+ �0n4n)+ (�1141+ :::+ �1n4n) � g. Thus,

the restricted model, with cjk(�:g;�Supply) can duplicate the more general model if 0 = �0141+ :::+�0n4nand 1 = �1141 + :::+ �1n4n.

10.4 Estimation

10.4.1 Demand

Construction of Demand Moments Under the assumption that the horizontal shock to preferences,

"mijk, is a type-1 logit error, the probability that individual i enrolls in j0k0 in market m, conditional on i0s

unobserved type, �i, can be written as:

Prob(j0k0j�i;m;�) =e(1+�1i)�gj0k0�(�+�pIm+�pi)�pj0k0+�j0

1 +P

j2m

Pk2mj

e(1+�1i)�gjk�(�+�pIm+�pi)�pjk+�j

=euij0k0+�j0

1 +P

j2m

Pk2mj

euijk+�j

where m is the set of �rms that have entered market m and jm is the set of products o¤ered by each

�rm j that is participating in market m:

Three other probability functions are used in estimation. The probability that consumer i enrolls in a

45

product o¤ered by �rm j0 in market m can be written by summing over Prob(j0k0j�i) for each k0 2 jm :

Prob(j0j�i;m;�) =

Pk02j0m

euij0k0+�j0

1 +P

j2m

Pk2mj

euijk+�j

The probability of i enrolling in product k0 conditional on enrolling in �rm j0 can be written as:

Prob(k0jj0; �i;m;�) =euij0k0P

k2mj0

euijk

Note that �rm level �j0 falls out of Prob(k0jj0; �i;m;�).

The probability of i enrolling in product j0k0 in market m0, and then product ejek one year later in marketem can be written as:

Prob(j0k0;ejekj�i;m0; em;�) = euij0k0+�j0

1 +P

j2m

Pk2mj

euijk+�j� euiejek+�ej01 +

Pj2fm

Pk2fmj

euijk+�j

It is necessary to work with the unconditional share probabilities. These are obtained simply by inte-

grating over Prob(j0k0j�i) and Prob(jj�i) with respect to �:

Prob(j0k0jm;�) =Z�

euij0k0+�j0

eui0 +P

j2m

Pk2mj

euijk+�jdF (vj�)

Prob(j0jm;�) =Z�

Pk02j0m

euij0k0+�j0

e�0i +P

j2m

Pk2mj

euijk+�jdF (vj�)

Prob(k0jj0;m;�) =Z�

euij0k0+�j0Pk2mj0

euijk+�jdF (vj�)

Prob(j0k0;ejekjm;�) = Z�

euij0k0+�j0

1 +P

j2m

Pk2mj

euijk+�j� euiejek+�ej01 +

Pj2fm

Pk2fmj

euijk+�jdF (vj�)

With a set of L random draws from f(vj�) I simulate the above probabilities with [Prob(j0k0jm;�) =

1L

LXl=1

euij0k0+�j0

eui0+P

j2m

Pk2mj

euijk+�j; [Prob(j0jm;�) = 1

L

LXl=1

Pk02

j0m

euij0k0+�j0

e�0i+P

j2m

Pk2mj

euijk+�j; and[Prob(k0jj0;m;�) = 1

L

LXl=1

euij0k0+�j0P

k2mj0

euijk+�j:

All moments are constructed using these simulated probabilities.

Three forms of moment conditions are used in estimation. The population moments, described in the

main text are repeated below:

E[xjk � (dijk � Prob(kjj;m;�))jij] = 0 (11)

46

E[xjkl � x0j0k0 � (dijk;j0k0 � Prob(jk&j0k0jm;m0;�))ji] = 0 (12)

E[f(x�jkjxjk) � (dijk � Prob(kjj;m;�))jij] = 0 (13)

The corresponding sample moments are:

1

Nj

NjXj=1

1

jjmj

jjmjXk=1

xjkpnjm

Xi

[Prob(kjj;m;�)� dijk] = 0

1

M

MXi=1

1

jmj � jm0 jX

jk2m

Xj0k02m0

xjkx0j0k0 � (Prob(jk; j0k0jm;�)� di;jk;j0k0) = 0

1

Nj

NjXj=1

1

jjmj

jjmjXk=1

f(x�jkjxjk)pnjm

Xi

[Prob(kjj;m;�)� dijk] = 0

Above, j sums over insurers, k over products and i over MCBS respondents. These summations are

divided through bypnjm instead of njm to ensure that the variance of residuals interacted with instruments

( 1pnjm

Pi[Prob(kjj;m;�) � dijk]) does not depend on the number of survey respondents from each �rm.

This leads to more weight being placed on contracts for whom we observe more individuals enrolling.

Accounting for Simulation Error Consider a sample moment condition employed in demand:

1

Nj

NjXj=1

1

jjmj

jjmjXk=1

Zjkpnjm

Xi

[Prob(kjj;m;�)� dijk] = 0

where Prob(kjj;m;�) is the true probability of enrolling in product k conditional on enrolling in �rm j:

Rewrite this moment condition, using [Probm(kjj;m;�) to represent simulated probabilities:

1

Nj

NjXj=1

1

jjmj

jjmjXk=1

Zjkpnjm

Xi

[Prob(kjj;m;�)

�[Prob(kjj;m;�) +[Prob(kjj;m;�)� dijk] =

1

Nj

NjXj=1

1

jjmj

jjmjXk=1

Zjkpnjm

Xi

[Prob(kjj;m;�)�[Prob(kjj;m;�)]

+1

Nj

NjXj=1

1

jjmj

jjmjXk=1

Zjkpnjm

Xi

[[Prob(kjj;m;�)� dijk] = 0

Because simulation error is independent of the randomness inherent toP

i[[Prob(kjj;m;�) � dijk], the

variance of the sample moment is equal to:

47

V ar

24 1

Nj

NjXj=1

1

jjmj

jjmjXk=1

Zjkpnjm

Xi

[Prob(kjj;m;�)�[Prob(kjj;m;�)]

35+V ar

24 1

Nj

NjXj=1

1

jjmj

jjmjXk=1

Zjkpnjm

Xi

[[Prob(kjj;m;�)� dijk]

35The �rst term is variance due to simulation error. Note that [Probm(kjj;m;�)] is the sum of nsim draws

of Prob(kjj; �i;m;�)] where �i is distributed according to F (vj�). Because E (Prob(kjj; �i;m;�)]) =

Prob(kjj;m;�), the delta method implies:

[Probm(kjj; �i;m;�)]� Prob(kjj;m;�)~N(0;@[Probm(kjj; �i;m;�)]

@��@[Probm(kjj; �i;m;�)]

@�0)

Using this result, it is straightforward to construct the variance of1Nj

PNj

j=11

jjmjPjjmj

k=1Zjkpnjm

Pi[Prob(kjj;m;�)�[Probm(kjj;m;�)]. Analogous procedures can be used

for the remaining moments.

Selection in Demand Moments Consider a moment condition that interacts Zjk with the random

residuals,P

i[Prob(kjj;m;�)� dijk] . Assume for a particular �rm j that Zjk = Zj for all k: That �rm�s

contribution to the sample moment condition is equal to zero, regardless of the choice of parameters:

1

jjmj

jjmjXk=1

Zjpnjm

Xi

[Prob(kjj;m;�)� dijk] =

Zjpnjm

jjmj

jjmjXk=1

1

njm

Xi

[Prob(kjj;m;�)� dijk] =

Zjjjmj

1pnjm

jjmjXk=1

(Prob(kjj;m;�)� 1

njm

Xi

dijk) =

Zjjjmj

1pnjm

� [jjmjXk=1

(Prob(kjj;m;�)�jjmjXk=1

1

njm

Xi

dijk] =

Zjjjmj

1pnjm

� [1� 1] = 0

To model this selection issue, let sjZ be an indicator variable that equals one if and only if there is

variation in Zjk across k. Interacting sjZ with Z and yields the following moment condition:

1

Nj

NjXj=1

1

jjmj

jjmjXk=1

sjZ � Zjkpnjm

Xi

[Prob(kjj;m;�)� dijk]

48

This sample moment condition should equal zero in expectation only if for each �rm,

E

24jjmjXk=1

sjZ � Zjkpnjm

Xi

[Prob(kjj;m;�)� dijk]

35 = 0The discussion in Wooldridge (pg 573), argues that the selection case here is of the most favorable kind.

Note that sjZ is a deterministic function of the instruments themselves, and therefore E [sjZ(Z) � Zjk � �jk] =

0 if E [�jk j Z] = 0 via iterated expectations. That is indeed the case, and therefore, the sample moment

conditions still equal zero in expectation.

10.4.2 Supply

Recall that in each market the collection of plan characteristics, fgjk; pjkgjk2m satisfy a Nash Equilibrium.

Therefore, all �rms��rst order conditions with respect premiums and insurance generosity must equal zero:

@Profitj@gjk

=@Profitj@pjk

= 0 8 j; k

Backing out cost shocks Firms��rst order conditions for pjk and gjk reduce to the following set of

linear equations. First, for the �rst order condition on premium:

@ Pr ofitjkm@pjk0

= c0pjk0 +

mjXk=1

2Xz=0

ck;zpjk0 � zjk = 0

where

c0pjk0 =

Z�

mjXk=1

@MSjk(g; p; �jG;P;�Demand)@pjk0

� [Sm + pjk � 00 � �]

� 01 � � � gjk]dF (�; #)

+

Z�

MSjk0(g; p; �jG;P;�Demand)dF (�j�)

ck;0pjk0 = �Z�

@MSjk(g; p; �jG;P;�Demand)@pjk0

dF (�j�) 8 k

ck;1pjk0 = �gjkZ�

@MSjk(g; p; �jG;P;�Demand)@pjk0

dF (�j�) 8 k

and below is the �rst order condition on quality:

49

@ Pr ofitjkm@gjk0

= c0gjk0 +

mjXk=1

1Xz=0

ck;zgjk01 � 1jk0 = 0

where

c0gjk01 =

Z�

mjXk=1

@MSjk(g; p; �jG;P;�Demand)@gjk01

� [Sm + pjk � 00 � � � 01 � � � gjk0 ]dF (�; #)

�Z�

MSjk0(g; p; �jG;P;�Demand) � (�1 + 01 � � + �01 � [Xm Zjm])dF (�; #)

ck;1gjk01 = �gjkZ�

@MSjk(g; p; �jG;P;�Demand)@gjk0

dF (�; #) 8 k 6= k0

ck0;1gjk01

= �gjk0Z�

@MSjk0(g; p; �jG;P;�Demand)@gjk0

dF (�; #) �Z�

MSjk0(g; p; �jG;P;�Demand)dF (�; #)

By inspection, these linear equations are non-redundant. Backing out unobserved cost shocks is done

via the following matrix algebra:

0BBBBBBBBBBBB@

e 0j1e 1j1�

�e 0jmje 1jmj

1CCCCCCCCCCCCA= �1 �

0BBBBBBBBBBBB@

c1;0pj1 c1;1pj1 � � cmj ;0pj1 c

mj ;0pj1

c1;0gj1 c1;1gj1 � � cmj ;0gj1 c

mj ;1gj1

� � � � � �

� � � � � �

c1;0pjmjc1;1pjmj

� � cmj ;0pjmj

cmj ;1pjmj

c1;0gjmjc1;1gjmj

� � cmj ;0gjmj

cmj ;1gjmj

1CCCCCCCCCCCCA

�1

�

0BBBBBBBBBBBB@

c0pj1

c0gj1

�

�

c0pjmj

c0gjmj

1CCCCCCCCCCCCAConstruction of Supply Side Moments Supply side moments are constructed by exploiting assumed

population moment conditions relating �rms�unobserved costs shocks to instruments. These conditions are:

E[ njk] = 0 8 jkn

E[Xm � njk] = 0 8 jkn

E[Zj � njk] = 0 8 jkn

50

E[f(Z 0�jm) � njk] = 0 8 j; k; n

E[NProd;m � njk] = 0 8 j; k; n

E[NFirm;m � njk] = 0 8 j; k; n

E[f(Z 0�jm) �NProd;m � njk] = 0 8 j; k; n

E[f(Z 0�jm) �NFirm;m � njk] = 0 8 j; k; n

E[�j � njk] = 0 8 j; k; n

E[f(��j) � njk] = 0 8 j; k; n

The corresponding sample moment conditions are below. Notation is the same as above. Within each

�rm, the residual is constructed as 1pmj

Pmj

k=1 njk so that the variance does not depend on the number of

products o¤ered by �rm j, mj .

1

Nj

NjXj=1

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

X 0m �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

Z 0jm �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

f(Z 0�jm) �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

NPr od;m �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

NFirm;m �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

f(Z 0�jm) �NPr od;m �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

f(Z 0�jm) �NFirm;m �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

�j �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

1

Nj

NjXj=1

f(��j) �

1pmj

mjXk=1

njk

!= 0 8 j; k; n = 0; 1

51

Simulation Error in Supply Moments Simulation error is also present in the supply moments because

they are constructed from cost shocks which are non-linear functions of the simulated market share

functions. Because the simulation error enters each moment condition in a non-fashion, biases may be

present. Changing the number of simulation draws, however, does not have large e¤ects on parameter

estimates. To correct variance estimates for this simulation error, I repeatedly take samples of simulation

draws to simulate the variation of each moment condition due to simulation. As above, this variation is

independent of variation in the sample moments due to observable data, and in practice quite small. All

reported standard errors are corrected for this simulation error.

10.5 Properties of b�Following Newey & McFadden (1994) the following conditions are necessary for b� p! �0, where b� minimizesn(m;�) � (Mn (�)

0 �W �Mn(m;�).

1. (m;�) is uniquely minimized at �0

2. The parameter space � is compact.

3. (m;�) is continuous

4. n(m;�) converges uniformly in probability to (m;�):

The �rst two conditions are assumed. Mn (�) is highly non-linear, thus proving identi�cation is a

challenge. Intuition for identi�cation, however, is provided throughout the main text. Condition 3 is

satis�ed by simple inspection of moment conditions. All market share functions entering demand moments

are continuous functions over the entire parameter space �. Similarly, �rms��rst order conditions are all

continuously di¤erentiable at all �. Thus, the unobserved cost shocks, are continuous functions of � since

inversion preserves continuity. Because Mn (�) is continuous for all �, so is M0(m;�) and (m;�). The

fourth condition is true under standard regularity conditions.

52